# mehlhorn

2024

[1]

B. Ray Chaudhury, J. Garg, and K. Mehlhorn, “EFX Exists for Three Agents,” Journal of the ACM, vol. 71, no. 1, 2024.

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BibTeX

@article{RayChaudhury24,
TITLE = {{EFX} Exists for Three Agents},
AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0004-5411},
DOI = {10.1145/3616009},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2024},
DATE = {2024},
JOURNAL = {Journal of the ACM},
VOLUME = {71},
NUMBER = {1},
PAGES = {1--27},
EID = {4},
}

Endnote

%0 Journal Article
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T EFX Exists for Three Agents :
%G eng
%U http://hdl.handle.net/21.11116/0000-000E-6961-F
%R 10.1145/3616009
%D 2024
%J Journal of the ACM
%V 71
%N 1
%& 1
%P 1 - 27
%Z sequence number: 4
%I ACM
%C New York, NY
%@ false

2023

[2]

H. Akrami, N. Alon, B. Ray Chaudhury, J. Garg, K. Mehlhorn, and R. Mehta, “EFX: A Simpler Approach and an (Almost) Optimal Guarantee via Rainbow Cycle Number,” in EC 2023, 24th ACM Conference on Economics and Computation, London, UK, 2023.

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BibTeX

@inproceedings{Akrami_EC23,
TITLE = {{EFX}: {A} Simpler Approach and an (Almost) Optimal Guarantee via Rainbow Cycle Number},
AUTHOR = {Akrami, Hannaneh and Alon, Noga and Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta},
LANGUAGE = {eng},
ISBN = {979-8-4007-0104-7},
DOI = {10.1145/3580507.3597799},
PUBLISHER = {ACM},
YEAR = {2023},
MARGINALMARK = {$\bullet$},
DATE = {2023},
BOOKTITLE = {EC 2023, 24th ACM Conference on Economics and Computation},
PAGES = {61--61},
ADDRESS = {London, UK},
}

Endnote

%0 Conference Proceedings
%A Akrami, Hannaneh
%A Alon, Noga
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%A Mehta, Ruta
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T EFX: A Simpler Approach and an (Almost) Optimal Guarantee via Rainbow Cycle Number :
%G eng
%U http://hdl.handle.net/21.11116/0000-000F-1437-D
%R 10.1145/3580507.3597799
%D 2023
%B 24th ACM Conference on Economics and Computation
%Z date of event: 2023-07-09 - 2023-07-12
%C London, UK
%B EC 2023
%P 61 - 61
%I ACM
%@ 979-8-4007-0104-7

[3]

H. Akrami, B. Ray Chaudhury, J. Garg, K. Mehlhorn, and R. Mehta, “Fair and Efficient Allocation of Indivisible Chores with Surplus,” in Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence (IJCAI 2023), Macao, 2023.

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BibTeX

@inproceedings{Akrami_IJCAI2023b,
TITLE = {Fair and Efficient Allocation of Indivisible Chores with Surplus},
AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta},
LANGUAGE = {eng},
ISBN = {978-1-956792-03-4},
DOI = {10.24963/ijcai.2023/277},
PUBLISHER = {IJCAI},
YEAR = {2023},
MARGINALMARK = {$\bullet$},
DATE = {2023},
BOOKTITLE = {Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence (IJCAI 2023)},
EDITOR = {Elkind, Edith},
PAGES = {2494--2502},
ADDRESS = {Macao},
}

Endnote

%0 Conference Proceedings
%A Akrami, Hannaneh
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%A Mehta, Ruta
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Fair and Efficient Allocation of Indivisible Chores with Surplus :
%G eng
%U http://hdl.handle.net/21.11116/0000-000F-1425-1
%R 10.24963/ijcai.2023/277
%D 2023
%B Thirty-Second International Joint Conference on Artificial Intelligence
%Z date of event: 2023-08-19 - 2023-08-25
%C Macao
%B Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence
%E Elkind, Edith
%P 2494 - 2502
%I IJCAI
%@ 978-1-956792-03-4
%U https://www.ijcai.org/proceedings/2023/277

[4]

H. Akrami, K. Mehlhorn, M. Seddighin, and G. Shahkarami, “Randomized and Deterministic Maximin-share Approximations for Fractionally Subadditive Valuations,” in Advances in Neural Information Processing Systems 36 (NeurIPS 2023), New Orleans, LA, USA, 2023.

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BibTeX

@inproceedings{Akrami_NeurIPS23,
TITLE = {Randomized and Deterministic Maximin-share Approximations for Fractionally Subadditive Valuations},
AUTHOR = {Akrami, Hannaneh and Mehlhorn, Kurt and Seddighin, Masoud and Shahkarami, Golnoosh},
LANGUAGE = {eng},
PUBLISHER = {Curran Associates, Inc},
YEAR = {2023},
MARGINALMARK = {$\bullet$},
DATE = {2023},
BOOKTITLE = {Advances in Neural Information Processing Systems 36 (NeurIPS 2023)},
EDITOR = {Oh, A. and Neumann, T. and Globerson, A. and Saenko, K. and Hartdt, M. and Levine, S.},
PAGES = {58821--58832},
ADDRESS = {New Orleans, LA, USA},
}

Endnote

%0 Conference Proceedings
%A Akrami, Hannaneh
%A Mehlhorn, Kurt
%A Seddighin, Masoud
%A Shahkarami, Golnoosh
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Randomized and Deterministic Maximin-share Approximations for Fractionally Subadditive Valuations :
%G eng
%U http://hdl.handle.net/21.11116/0000-000F-1435-F
%D 2023
%B Thirty-seventh Annual Conference on Neural Information Processing Systems
%Z date of event: 2023-12-10 - 2023-12-16
%C New Orleans, LA, USA
%B Advances in Neural Information Processing Systems 36
%E Oh, A.; Neumann, T.; Globerson, A.; Saenko, K.; Hartdt, M.; Levine, S.
%P 58821 - 58832
%I Curran Associates, Inc
%U https://proceedings.neurips.cc/paper_files/paper/2023/file/b7ed46bd87cd51d4c031b96d9b1a8eb6-Paper-Conference.pdf

[5]

J. Garg, M. Hoefer, and K. Mehlhorn, “Satiation in Fisher Markets and Approximation of Nash Social Welfare,” Mathematics of Operations Research, 2023.

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BibTeX

@article{Garg23x,
TITLE = {Satiation in {F}isher Markets and Approximation of {N}ash Social Welfare},
AUTHOR = {Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0364-765X},
DOI = {10.1287/moor.2019.0129},
PUBLISHER = {INFORMS},
YEAR = {2023},
MARGINALMARK = {$\bullet$},
JOURNAL = {Mathematics of Operations Research},
}

Endnote

%0 Journal Article
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Satiation in Fisher Markets and Approximation of Nash Social Welfare :
%G eng
%U http://hdl.handle.net/21.11116/0000-000D-944A-9
%R 10.1287/moor.2019.0129
%7 2023
%D 2023
%J Mathematics of Operations Research
%I INFORMS
%@ false

[6]

B. Ray Chaudhury, J. Garg, K. Mehlhorn, R. Mehta, and P. Misra, “Improving EFX Guarantees through Rainbow Cycle Number,” Mathematics of Operations Research, 2023.

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BibTeX

@article{RayChaudhury2023,
TITLE = {Improving {EFX} Guarantees through Rainbow Cycle Number},
AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta and Misra, Pranabendu},
LANGUAGE = {eng},
ISSN = {0364-765X},
DOI = {10.1287/moor.2021.0252},
PUBLISHER = {informs},
ADDRESS = {Catonsville, MD},
YEAR = {2023},
MARGINALMARK = {$\bullet$},
JOURNAL = {Mathematics of Operations Research},
}

Endnote

%0 Journal Article
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%A Mehta, Ruta
%A Misra, Pranabendu
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Improving EFX Guarantees through Rainbow Cycle Number :
%G eng
%U http://hdl.handle.net/21.11116/0000-000E-0D04-0
%R 10.1287/moor.2021.0252
%7 2023
%D 2023
%J Mathematics of Operations Research
%I informs
%C Catonsville, MD
%@ false

2022

[7]

H. Akrami, N. Alon, B. Ray Chaudhury, J. Garg, K. Mehlhorn, and R. Mehta, “EFX Allocations: Simplifications and Improvements,” 2022. [Online]. Available: https://arxiv.org/abs/2205.07638. (arXiv: 2205.07638)

Abstract

The existence of EFX allocations is a fundamental open problem in discrete<br>fair division. Given a set of agents and indivisible goods, the goal is to<br>determine the existence of an allocation where no agent envies another<br>following the removal of any single good from the other agent's bundle. Since<br>the general problem has been illusive, progress is made on two fronts: $(i)$<br>proving existence when the number of agents is small, $(ii)$ proving existence<br>of relaxations of EFX. In this paper, we improve results on both fronts (and<br>simplify in one of the cases).<br> We prove the existence of EFX allocations with three agents, restricting only<br>one agent to have an MMS-feasible valuation function (a strict generalization<br>of nice-cancelable valuation functions introduced by Berger et al. which<br>subsumes additive, budget-additive and unit demand valuation functions). The<br>other agents may have any monotone valuation functions. Our proof technique is<br>significantly simpler and shorter than the proof by Chaudhury et al. on<br>existence of EFX allocations when there are three agents with additive<br>valuation functions and therefore more accessible.<br> Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX<br>allocations and EFX allocations with few unallocated goods (charity). Chaudhury<br>et al. showed the existence of $(1-\epsilon)$-EFX allocation with<br>$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to a<br>problem in extremal combinatorics. We improve their result and prove the<br>existence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/<br>\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used<br>to prove improved upper-bounds on a problem in zero-sum combinatorics<br>introduced by Alon and Krivelevich.<br>

Export

BibTeX

@online{Akrami2205.07638,
TITLE = {{EFX} Allocations: Simplifications and Improvements},
AUTHOR = {Akrami, Hannaneh and Alon, Noga and Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2205.07638},
EPRINT = {2205.07638},
EPRINTTYPE = {arXiv},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
ABSTRACT = {The existence of EFX allocations is a fundamental open problem in discrete<br>fair division. Given a set of agents and indivisible goods, the goal is to<br>determine the existence of an allocation where no agent envies another<br>following the removal of any single good from the other agent's bundle. Since<br>the general problem has been illusive, progress is made on two fronts: $(i)$<br>proving existence when the number of agents is small, $(ii)$ proving existence<br>of relaxations of EFX. In this paper, we improve results on both fronts (and<br>simplify in one of the cases).<br> We prove the existence of EFX allocations with three agents, restricting only<br>one agent to have an MMS-feasible valuation function (a strict generalization<br>of nice-cancelable valuation functions introduced by Berger et al. which<br>subsumes additive, budget-additive and unit demand valuation functions). The<br>other agents may have any monotone valuation functions. Our proof technique is<br>significantly simpler and shorter than the proof by Chaudhury et al. on<br>existence of EFX allocations when there are three agents with additive<br>valuation functions and therefore more accessible.<br> Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX<br>allocations and EFX allocations with few unallocated goods (charity). Chaudhury<br>et al. showed the existence of $(1-\epsilon)$-EFX allocation with<br>$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to a<br>problem in extremal combinatorics. We improve their result and prove the<br>existence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/<br>\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used<br>to prove improved upper-bounds on a problem in zero-sum combinatorics<br>introduced by Alon and Krivelevich.<br>},
}

Endnote

%0 Report
%A Akrami, Hannaneh
%A Alon, Noga
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%A Mehta, Ruta
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T EFX Allocations: Simplifications and Improvements :
%G eng
%U http://hdl.handle.net/21.11116/0000-000C-1FEB-A
%U https://arxiv.org/abs/2205.07638
%D 2022
%X The existence of EFX allocations is a fundamental open problem in discrete<br>fair division. Given a set of agents and indivisible goods, the goal is to<br>determine the existence of an allocation where no agent envies another<br>following the removal of any single good from the other agent's bundle. Since<br>the general problem has been illusive, progress is made on two fronts: $(i)$<br>proving existence when the number of agents is small, $(ii)$ proving existence<br>of relaxations of EFX. In this paper, we improve results on both fronts (and<br>simplify in one of the cases).<br> We prove the existence of EFX allocations with three agents, restricting only<br>one agent to have an MMS-feasible valuation function (a strict generalization<br>of nice-cancelable valuation functions introduced by Berger et al. which<br>subsumes additive, budget-additive and unit demand valuation functions). The<br>other agents may have any monotone valuation functions. Our proof technique is<br>significantly simpler and shorter than the proof by Chaudhury et al. on<br>existence of EFX allocations when there are three agents with additive<br>valuation functions and therefore more accessible.<br> Secondly, we consider relaxations of EFX allocations, namely, approximate-EFX<br>allocations and EFX allocations with few unallocated goods (charity). Chaudhury<br>et al. showed the existence of $(1-\epsilon)$-EFX allocation with<br>$O((n/\epsilon)^{\frac{4}{5}})$ charity by establishing a connection to a<br>problem in extremal combinatorics. We improve their result and prove the<br>existence of $(1-\epsilon)$-EFX allocations with $\tilde{O}((n/<br>\epsilon)^{\frac{1}{2}})$ charity. In fact, some of our techniques can be used<br>to prove improved upper-bounds on a problem in zero-sum combinatorics<br>introduced by Alon and Krivelevich.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT

[8]

H. Akrami, B. Ray Chaudhury, M. Hoefer, K. Mehlhorn, M. Schmalhofer, G. Shahkarami, G. Varricchio, Q. Vermande, and E. van Wijland, “Maximizing Nash Social Welfare in 2-Value Instances,” in Proceedings of the 36th AAAI Conference on Artificial Intelligence, Virtual Conference, 2022.

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BibTeX

@inproceedings{AkramiAAAI22,
TITLE = {Maximizing {N}ash Social Welfare in 2-Value Instances},
AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Hoefer, Martin and Mehlhorn, Kurt and Schmalhofer, Marco and Shahkarami, Golnoosh and Varricchio, Giovanna and Vermande, Quentin and van Wijland, Ernest},
LANGUAGE = {eng},
ISBN = {978-1-57735-876-3},
DOI = {10.1609/aaai.v36i5.20402},
PUBLISHER = {AAAI},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
BOOKTITLE = {Proceedings of the 36th AAAI Conference on Artificial Intelligence},
PAGES = {4760--4767},
ADDRESS = {Virtual Conference},
}

Endnote

%0 Conference Proceedings
%A Akrami, Hannaneh
%A Ray Chaudhury, Bhaskar
%A Hoefer, Martin
%A Mehlhorn, Kurt
%A Schmalhofer, Marco
%A Shahkarami, Golnoosh
%A Varricchio, Giovanna
%A Vermande, Quentin
%A van Wijland, Ernest
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
%T Maximizing Nash Social Welfare in 2-Value Instances :
%G eng
%U http://hdl.handle.net/21.11116/0000-000C-1FC6-3
%R 10.1609/aaai.v36i5.20402
%D 2022
%B 36th AAAI Conference on Artificial Intelligence
%Z date of event: 2022-02-22 - 2022-03-01
%C Virtual Conference
%B Proceedings of the 36th AAAI Conference on Artificial Intelligence
%P 4760 - 4767
%I AAAI
%@ 978-1-57735-876-3
%U https://ojs.aaai.org/index.php/AAAI/article/view/20402

[9]

H. Akrami, B. Ray Chaudhury, M. Hoefer, K. Mehlhorn, M. Schmalhofer, G. Shahkarami, G. Varricchio, Q. Vermande, and E. van Wijland, “Maximizing Nash Social Welfare in 2-Value Instances: The Half-Integer Case,” 2022. [Online]. Available: https://arxiv.org/abs/2207.10949. (arXiv: 2207.10949)

Abstract

We consider the problem of maximizing the Nash social welfare when allocating<br>a set $G$ of indivisible goods to a set $N$ of agents. We study instances, in<br>which all agents have 2-value additive valuations: The value of a good $g \in<br>G$ for an agent $i \in N$ is either $1$ or $s$, where $s$ is an odd multiple of<br>$\frac{1}{2}$ larger than one. We show that the problem is solvable in<br>polynomial time. Akrami et at. showed that this problem is solvable in<br>polynomial time if $s$ is integral and is NP-hard whenever $s = \frac{p}{q}$,<br>$p \in \mathbb{N}$ and $q\in \mathbb{N}$ are co-prime and $p > q \ge 3$. For<br>the latter situation, an approximation algorithm was also given. It obtains an<br>approximation ratio of at most $1.0345$. Moreover, the problem is APX-hard,<br>with a lower bound of $1.000015$ achieved at $\frac{p}{q} = \frac{5}{4}$. The<br>case $q = 2$ and odd $p$ was left open.<br> In the case of integral $s$, the problem is separable in the sense that the<br>optimal allocation of the heavy goods (= value $s$ for some agent) is<br>independent of the number of light goods (= value $1$ for all agents). This<br>leads to an algorithm that first computes an optimal allocation of the heavy<br>goods and then adds the light goods greedily. This separation no longer holds<br>for $s = \frac{3}{2}$; a simple example is given in the introduction. Thus an<br>algorithm has to consider heavy and light goods together. This complicates<br>matters considerably. Our algorithm is based on a collection of improvement<br>rules that transfers any allocation into an optimal allocation and exploits a<br>connection to matchings with parity constraints.<br>

Export

BibTeX

@online{Akrami2207.10949,
TITLE = {Maximizing Nash Social Welfare in 2-Value Instances: The Half-Integer Case},
AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Hoefer, Martin and Mehlhorn, Kurt and Schmalhofer, Marco and Shahkarami, Golnoosh and Varricchio, Giovanna and Vermande, Quentin and van Wijland, Ernest},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2207.10949},
EPRINT = {2207.10949},
EPRINTTYPE = {arXiv},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
ABSTRACT = {We consider the problem of maximizing the Nash social welfare when allocating<br>a set $G$ of indivisible goods to a set $N$ of agents. We study instances, in<br>which all agents have 2-value additive valuations: The value of a good $g \in<br>G$ for an agent $i \in N$ is either $1$ or $s$, where $s$ is an odd multiple of<br>$\frac{1}{2}$ larger than one. We show that the problem is solvable in<br>polynomial time. Akrami et at. showed that this problem is solvable in<br>polynomial time if $s$ is integral and is NP-hard whenever $s = \frac{p}{q}$,<br>$p \in \mathbb{N}$ and $q\in \mathbb{N}$ are co-prime and $p > q \ge 3$. For<br>the latter situation, an approximation algorithm was also given. It obtains an<br>approximation ratio of at most $1.0345$. Moreover, the problem is APX-hard,<br>with a lower bound of $1.000015$ achieved at $\frac{p}{q} = \frac{5}{4}$. The<br>case $q = 2$ and odd $p$ was left open.<br> In the case of integral $s$, the problem is separable in the sense that the<br>optimal allocation of the heavy goods (= value $s$ for some agent) is<br>independent of the number of light goods (= value $1$ for all agents). This<br>leads to an algorithm that first computes an optimal allocation of the heavy<br>goods and then adds the light goods greedily. This separation no longer holds<br>for $s = \frac{3}{2}$; a simple example is given in the introduction. Thus an<br>algorithm has to consider heavy and light goods together. This complicates<br>matters considerably. Our algorithm is based on a collection of improvement<br>rules that transfers any allocation into an optimal allocation and exploits a<br>connection to matchings with parity constraints.<br>},
}

Endnote

%0 Report
%A Akrami, Hannaneh
%A Ray Chaudhury, Bhaskar
%A Hoefer, Martin
%A Mehlhorn, Kurt
%A Schmalhofer, Marco
%A Shahkarami, Golnoosh
%A Varricchio, Giovanna
%A Vermande, Quentin
%A van Wijland, Ernest
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
%T Maximizing Nash Social Welfare in 2-Value Instances: The Half-Integer
Case :
%G eng
%U http://hdl.handle.net/21.11116/0000-000C-1FD5-2
%U https://arxiv.org/abs/2207.10949
%D 2022
%X We consider the problem of maximizing the Nash social welfare when allocating<br>a set $G$ of indivisible goods to a set $N$ of agents. We study instances, in<br>which all agents have 2-value additive valuations: The value of a good $g \in<br>G$ for an agent $i \in N$ is either $1$ or $s$, where $s$ is an odd multiple of<br>$\frac{1}{2}$ larger than one. We show that the problem is solvable in<br>polynomial time. Akrami et at. showed that this problem is solvable in<br>polynomial time if $s$ is integral and is NP-hard whenever $s = \frac{p}{q}$,<br>$p \in \mathbb{N}$ and $q\in \mathbb{N}$ are co-prime and $p > q \ge 3$. For<br>the latter situation, an approximation algorithm was also given. It obtains an<br>approximation ratio of at most $1.0345$. Moreover, the problem is APX-hard,<br>with a lower bound of $1.000015$ achieved at $\frac{p}{q} = \frac{5}{4}$. The<br>case $q = 2$ and odd $p$ was left open.<br> In the case of integral $s$, the problem is separable in the sense that the<br>optimal allocation of the heavy goods (= value $s$ for some agent) is<br>independent of the number of light goods (= value $1$ for all agents). This<br>leads to an algorithm that first computes an optimal allocation of the heavy<br>goods and then adds the light goods greedily. This separation no longer holds<br>for $s = \frac{3}{2}$; a simple example is given in the introduction. Thus an<br>algorithm has to consider heavy and light goods together. This complicates<br>matters considerably. Our algorithm is based on a collection of improvement<br>rules that transfers any allocation into an optimal allocation and exploits a<br>connection to matchings with parity constraints.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT

[10]

V. Bonifaci, E. Facca, F. Folz, A. Karrenbauer, P. Kolev, K. Mehlhorn, G. Morigi, G. Shahkarami, and Q. Vermande, “Physarum-inspired Multi-commodity Flow Dynamics,” Theoretical Computer Science, vol. 920, 2022.

Export

BibTeX

@article{Bonifaci2022,
TITLE = {Physarum-inspired Multi-commodity Flow Dynamics},
AUTHOR = {Bonifaci, Vincenzo and Facca, Enrico and Folz, Frederic and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt and Morigi, Giovanna and Shahkarami, Golnoosh and Vermande, Quentin},
LANGUAGE = {eng},
ISSN = {0304-3975},
DOI = {10.1016/j.tcs.2022.02.001},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
DATE = {2022},
JOURNAL = {Theoretical Computer Science},
VOLUME = {920},
PAGES = {1--20},
}

Endnote

%0 Journal Article
%A Bonifaci, Vincenzo
%A Facca, Enrico
%A Folz, Frederic
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%A Morigi, Giovanna
%A Shahkarami, Golnoosh
%A Vermande, Quentin
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Physarum-inspired Multi-commodity Flow Dynamics :
%G eng
%U http://hdl.handle.net/21.11116/0000-000A-28A1-3
%R 10.1016/j.tcs.2022.02.001
%7 2022
%D 2022
%J Theoretical Computer Science
%V 920
%& 1
%P 1 - 20
%I Elsevier
%C Amsterdam
%@ false

[11]

Y. Gao, H. Kamkari, A. Karrenbauer, K. Mehlhorn, and M. Sharifi, “Physarum Inspired Dynamics to Solve Semi-Definite Programs,” 2022. [Online]. Available: https://arxiv.org/abs/2111.02291. (arXiv: 2111.02291)

Abstract

Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br>

Export

BibTeX

@online{Kamkari_2111.02291,
TITLE = {Physarum Inspired Dynamics to Solve Semi-Definite Programs},
AUTHOR = {Gao, Yuan and Kamkari, Hamidreza and Karrenbauer, Andreas and Mehlhorn, Kurt and Sharifi, Mohammadamin},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2111.02291},
EPRINT = {2111.02291},
EPRINTTYPE = {arXiv},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
ABSTRACT = {Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br>},
}

Endnote

%0 Report
%A Gao, Yuan
%A Kamkari, Hamidreza
%A Karrenbauer, Andreas
%A Mehlhorn, Kurt
%A Sharifi, Mohammadamin
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Physarum Inspired Dynamics to Solve Semi-Definite Programs :
%G eng
%U http://hdl.handle.net/21.11116/0000-0009-B656-9
%U https://arxiv.org/abs/2111.02291
%D 2022
%X Physarum Polycephalum is a Slime mold that can solve the shortest path<br>problem. A mathematical model based on the Physarum's behavior, known as the<br>Physarum Directed Dynamics, can solve positive linear programs. In this paper,<br>we will propose a Physarum based dynamic based on the previous work and<br>introduce a new way to solve positive Semi-Definite Programming (SDP) problems,<br>which are more general than positive linear programs. Empirical results suggest<br>that this extension of the dynamic can solve the positive SDP showing that the<br>nature-inspired algorithm can solve one of the hardest problems in the<br>polynomial domain. In this work, we will formulate an accurate algorithm to<br>solve positive and some non-negative SDPs and formally prove some key<br>characteristics of this solver thus inspiring future work to try and refine<br>this method.<br>
%K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Optimization and Control, math.OC

[12]

D. Halperin, S. Har-Peled, K. Mehlhorn, E. Oh, and M. Sharir, “The Maximum-Level Vertex in an Arrangement of Lines,” Discrete & Computational Geometry, vol. 67, 2022.

Export

BibTeX

@article{Halperin2022,
TITLE = {The Maximum-Level Vertex in an Arrangement of Lines},
AUTHOR = {Halperin, Dan and Har-Peled, Sariel and Mehlhorn, Kurt and Oh, Eunjin and Sharir, Micha},
LANGUAGE = {eng},
ISSN = {0179-5376},
DOI = {10.1007/s00454-021-00338-9},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
JOURNAL = {Discrete \& Computational Geometry},
VOLUME = {67},
PAGES = {439--461},
}

Endnote

%0 Journal Article
%A Halperin, Dan
%A Har-Peled, Sariel
%A Mehlhorn, Kurt
%A Oh, Eunjin
%A Sharir, Micha
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T The Maximum-Level Vertex in an Arrangement of Lines :
%G eng
%U http://hdl.handle.net/21.11116/0000-0009-D020-7
%R 10.1007/s00454-021-00338-9
%7 2022
%D 2022
%J Discrete & Computational Geometry
%V 67
%& 439
%P 439 - 461
%I Springer
%C New York, NY
%@ false
%U https://rdcu.be/cFlQF

[13]

B. Ray Chaudhury, Y. K. Cheung, J. Garg, N. Garg, M. Hoefer, and K. Mehlhorn, “Fair Division of Indivisible Goods for a Class of Concave Valuations,” Journal of Artificial Intelligence Research, vol. 74, 2022.

Export

BibTeX

@article{RayChaudhury22,
TITLE = {Fair Division of Indivisible Goods for a Class of Concave Valuations},
AUTHOR = {Ray Chaudhury, Bhaskar and Cheung, Yun Kuen and Garg, Jugal and Garg, Naveen and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1076-9757},
DOI = {10.1613/jair.1.12911},
PUBLISHER = {AI Access Foundation},
ADDRESS = {S.l.},
YEAR = {2022},
MARGINALMARK = {$\bullet$},
JOURNAL = {Journal of Artificial Intelligence Research},
VOLUME = {74},
PAGES = {111--142},
}

Endnote

%0 Journal Article
%A Ray Chaudhury, Bhaskar
%A Cheung, Yun Kuen
%A Garg, Jugal
%A Garg, Naveen
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Fair Division of Indivisible Goods for a Class of Concave Valuations :
%G eng
%U http://hdl.handle.net/21.11116/0000-000A-9DB8-6
%R 10.1613/jair.1.12911
%7 2022
%D 2022
%J Journal of Artificial Intelligence Research
%V 74
%& 111
%P 111 - 142
%I AI Access Foundation
%C S.l.
%@ false

2021

[14]

H. Akrami, B. Ray Chaudhury, M. Hoefer, K. Mehlhorn, M. Schmalhofer, G. Shahkarami, G. Varricchio, Q. Vermande, and E. van Wijland, “Maximizing Nash Social Welfare in 2-Value Instances,” 2021. [Online]. Available: https://arxiv.org/abs/2107.08965. (arXiv: 2107.08965)

Abstract

We consider the problem of maximizing the Nash social welfare when allocating<br>a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We<br>study instances, in which all agents have 2-value additive valuations: The<br>value of every agent $i \in \mathcal{N}$ for every good $j \in \mathcal{G}$ is<br>$v_{ij} \in \{p,q\}$, for $p,q \in \mathbb{N}$, $p \le q$. Maybe surprisingly,<br>we design an algorithm to compute an optimal allocation in polynomial time if<br>$p$ divides $q$, i.e., when $p=1$ and $q \in \mathbb{N}$ after appropriate<br>scaling. The problem is \classNP-hard whenever $p$ and $q$ are coprime and $p<br>\ge 3$.<br> In terms of approximation, we present positive and negative results for<br>general $p$ and $q$. We show that our algorithm obtains an approximation ratio<br>of at most 1.0345. Moreover, we prove that the problem is \classAPX-hard, with<br>a lower bound of $1.000015$ achieved at $p/q = 4/5$.<br>

Export

BibTeX

@online{Akrami2107.08965,
TITLE = {Maximizing Nash Social Welfare in 2-Value Instances},
AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Hoefer, Martin and Mehlhorn, Kurt and Schmalhofer, Marco and Shahkarami, Golnoosh and Varricchio, Giovanna and Vermande, Quentin and van Wijland, Ernest},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2107.08965},
EPRINT = {2107.08965},
EPRINTTYPE = {arXiv},
YEAR = {2021},
MARGINALMARK = {$\bullet$},
ABSTRACT = {We consider the problem of maximizing the Nash social welfare when allocating<br>a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We<br>study instances, in which all agents have 2-value additive valuations: The<br>value of every agent $i \in \mathcal{N}$ for every good $j \in \mathcal{G}$ is<br>$v_{ij} \in \{p,q\}$, for $p,q \in \mathbb{N}$, $p \le q$. Maybe surprisingly,<br>we design an algorithm to compute an optimal allocation in polynomial time if<br>$p$ divides $q$, i.e., when $p=1$ and $q \in \mathbb{N}$ after appropriate<br>scaling. The problem is \classNP-hard whenever $p$ and $q$ are coprime and $p<br>\ge 3$.<br> In terms of approximation, we present positive and negative results for<br>general $p$ and $q$. We show that our algorithm obtains an approximation ratio<br>of at most 1.0345. Moreover, we prove that the problem is \classAPX-hard, with<br>a lower bound of $1.000015$ achieved at $p/q = 4/5$.<br>},
}

Endnote

%0 Report
%A Akrami, Hannaneh
%A Ray Chaudhury, Bhaskar
%A Hoefer, Martin
%A Mehlhorn, Kurt
%A Schmalhofer, Marco
%A Shahkarami, Golnoosh
%A Varricchio, Giovanna
%A Vermande, Quentin
%A van Wijland, Ernest
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
%T Maximizing Nash Social Welfare in 2-Value Instances :
%G eng
%U http://hdl.handle.net/21.11116/0000-000C-2000-F
%U https://arxiv.org/abs/2107.08965
%D 2021
%X We consider the problem of maximizing the Nash social welfare when allocating<br>a set $\mathcal{G}$ of indivisible goods to a set $\mathcal{N}$ of agents. We<br>study instances, in which all agents have 2-value additive valuations: The<br>value of every agent $i \in \mathcal{N}$ for every good $j \in \mathcal{G}$ is<br>$v_{ij} \in \{p,q\}$, for $p,q \in \mathbb{N}$, $p \le q$. Maybe surprisingly,<br>we design an algorithm to compute an optimal allocation in polynomial time if<br>$p$ divides $q$, i.e., when $p=1$ and $q \in \mathbb{N}$ after appropriate<br>scaling. The problem is \classNP-hard whenever $p$ and $q$ are coprime and $p<br>\ge 3$.<br> In terms of approximation, we present positive and negative results for<br>general $p$ and $q$. We show that our algorithm obtains an approximation ratio<br>of at most 1.0345. Moreover, we prove that the problem is \classAPX-hard, with<br>a lower bound of $1.000015$ achieved at $p/q = 4/5$.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT

[15]

H. Akrami, B. Ray Chaudhury, K. Mehlhorn, G. Shahkarami, and Q. Vermande, “Nash Social Welfare for 2-value Instances,” 2021. [Online]. Available: https://arxiv.org/abs/2106.14816. (arXiv: 2106.14816)

Abstract

We study the problem of allocating a set of indivisible goods among agents<br>with 2-value additive valuations. Our goal is to find an allocation with<br>maximum Nash social welfare, i.e., the geometric mean of the valuations of the<br>agents. We give a polynomial-time algorithm to find a Nash social welfare<br>maximizing allocation when the valuation functions are integrally 2-valued,<br>i.e., each agent has a value either $1$ or $p$ for each good, for some positive<br>integer $p$. We then extend our algorithm to find a better approximation factor<br>for general 2-value instances.<br>

Export

BibTeX

@online{Akrami2106.14816,
TITLE = {Nash Social Welfare for 2-value Instances},
AUTHOR = {Akrami, Hannaneh and Ray Chaudhury, Bhaskar and Mehlhorn, Kurt and Shahkarami, Golnoosh and Vermande, Quentin},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2106.14816},
EPRINT = {2106.14816},
EPRINTTYPE = {arXiv},
YEAR = {2021},
MARGINALMARK = {$\bullet$},
ABSTRACT = {We study the problem of allocating a set of indivisible goods among agents<br>with 2-value additive valuations. Our goal is to find an allocation with<br>maximum Nash social welfare, i.e., the geometric mean of the valuations of the<br>agents. We give a polynomial-time algorithm to find a Nash social welfare<br>maximizing allocation when the valuation functions are integrally 2-valued,<br>i.e., each agent has a value either $1$ or $p$ for each good, for some positive<br>integer $p$. We then extend our algorithm to find a better approximation factor<br>for general 2-value instances.<br>},
}

Endnote

%0 Report
%A Akrami, Hannaneh
%A Ray Chaudhury, Bhaskar
%A Mehlhorn, Kurt
%A Shahkarami, Golnoosh
%A Vermande, Quentin
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Nash Social Welfare for 2-value Instances :
%G eng
%U http://hdl.handle.net/21.11116/0000-0008-DB45-4
%U https://arxiv.org/abs/2106.14816
%D 2021
%X We study the problem of allocating a set of indivisible goods among agents<br>with 2-value additive valuations. Our goal is to find an allocation with<br>maximum Nash social welfare, i.e., the geometric mean of the valuations of the<br>agents. We give a polynomial-time algorithm to find a Nash social welfare<br>maximizing allocation when the valuation functions are integrally 2-valued,<br>i.e., each agent has a value either $1$ or $p$ for each good, for some positive<br>integer $p$. We then extend our algorithm to find a better approximation factor<br>for general 2-value instances.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT

[16]

B. R. Chaudhury, J. Garg, K. Mehlhorn, R. Mehta, and P. Misra, “Improving EFX Guarantees through Rainbow Cycle Number,” in EC ’21, 22nd ACM Conference on Economics and Computation, Budapest, Hungary (Virtual), 2021.

Export

BibTeX

@inproceedings{Chaudhury_EC2021,
TITLE = {Improving {EFX} Guarantees through Rainbow Cycle Number},
AUTHOR = {Chaudhury, Bhaskar Ray and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta and Misra, Pranabendu},
LANGUAGE = {eng},
ISBN = {978-1-4503-8554-1},
DOI = {10.1145/3465456.3467605},
PUBLISHER = {ACM},
YEAR = {2021},
MARGINALMARK = {$\bullet$},
BOOKTITLE = {EC '21, 22nd ACM Conference on Economics and Computation},
EDITOR = {Bir{\'o}, P{\'e}ter and Chawla, Shuchi and Echenique, Federico and Sodomka, Eric},
PAGES = {310--311},
ADDRESS = {Budapest, Hungary (Virtual)},
}

Endnote

%0 Conference Proceedings
%A Chaudhury, Bhaskar Ray
%A Garg, Jugal
%A Mehlhorn, Kurt
%A Mehta, Ruta
%A Misra, Pranabendu
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improving EFX Guarantees through Rainbow Cycle Number :
%G eng
%U http://hdl.handle.net/21.11116/0000-0009-B3F6-7
%R 10.1145/3465456.3467605
%D 2021
%B 22nd ACM Conference on Economics and Computation
%Z date of event: 2021-07-18 - 2021-07-23
%C Budapest, Hungary (Virtual)
%B EC '21
%E Biró, Péter; Chawla, Shuchi; Echenique, Federico; Sodomka, Eric
%P 310 - 311
%I ACM
%@ 978-1-4503-8554-1

[17]

F. Folz, K. Mehlhorn, and G. Morigi, “Interplay of Periodic Dynamics and Noise: Insights from a Simple Adaptive System,” Physical Review E, vol. 104, no. 5, 2021.

Export

BibTeX

@article{Folz2021,
TITLE = {Interplay of Periodic Dynamics and Noise: {I}nsights from a Simple Adaptive System},
AUTHOR = {Folz, Frederic and Mehlhorn, Kurt and Morigi, Giovanna},
LANGUAGE = {eng},
ISSN = {1539-3755},
DOI = {10.1103/PhysRevE.104.054215},
PUBLISHER = {American Physical Society},
ADDRESS = {Melville, NY},
YEAR = {2021},
MARGINALMARK = {$\bullet$},
DATE = {2021},
JOURNAL = {Physical Review E},
VOLUME = {104},
NUMBER = {5},
EID = {054215},
}

Endnote

%0 Journal Article
%A Folz, Frederic
%A Mehlhorn, Kurt
%A Morigi, Giovanna
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Interplay of Periodic Dynamics and Noise: Insights from a Simple Adaptive System :
%G eng
%U http://hdl.handle.net/21.11116/0000-0009-9D3F-1
%R 10.1103/PhysRevE.104.054215
%7 2021
%D 2021
%J Physical Review E
%O Phys. Rev. E
%V 104
%N 5
%Z sequence number: 054215
%I American Physical Society
%C Melville, NY
%@ false

[18]

B. Ray Chaudhury, J. Garg, K. Mehlhorn, R. Mehta, and P. Misra, “Improving EFX Guarantees through Rainbow Cycle Number,” 2021. [Online]. Available: https://arxiv.org/abs/2103.01628. (arXiv: 2103.01628)

Abstract

We study the problem of fairly allocating a set of indivisible goods among<br>$n$ agents with additive valuations. Envy-freeness up to any good (EFX) is<br>arguably the most compelling fairness notion in this context. However, the<br>existence of EFX allocations has not been settled and is one of the most<br>important problems in fair division. Towards resolving this problem, many<br>impressive results show the existence of its relaxations, e.g., the existence<br>of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated<br>goods. The latter result was recently improved for three agents, in which the<br>two unallocated goods are allocated through an involved procedure. Reducing the<br>number of unallocated goods for arbitrary number of agents is a systematic way<br>to settle the big question. In this paper, we develop a new approach, and show<br>that for every $\varepsilon \in (0,1/2]$, there always exists a<br>$(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and<br>high Nash welfare.<br> For this, we reduce the EFX problem to a novel problem in extremal graph<br>theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d<br>\in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite<br>digraph $G =(\cup_{i \in [k]} V_i, E)$, in which<br> 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for<br>all $i \in [k]$,<br> 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming<br>edge from some vertex in $V_j$ and vice-versa, and<br> 3) there exists no cycle in $G$ that contains at most one vertex from each<br>part.<br> We show that any upper bound on $R(d)$ directly translates to a sublinear<br>bound on the number of unallocated goods. We establish a polynomial upper bound<br>on $R(d)$, yielding our main result. Furthermore, our approach is constructive,<br>which also gives a polynomial-time algorithm for finding such an allocation.<br>

Export

BibTeX

@online{RayChaudhury2103.01628,
TITLE = {Improving {EFX} Guarantees through Rainbow Cycle Number},
AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt and Mehta, Ruta and Misra, Pranabendu},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2103.01628},
EPRINT = {2103.01628},
EPRINTTYPE = {arXiv},
YEAR = {2021},
MARGINALMARK = {$\bullet$},
ABSTRACT = {We study the problem of fairly allocating a set of indivisible goods among<br>$n$ agents with additive valuations. Envy-freeness up to any good (EFX) is<br>arguably the most compelling fairness notion in this context. However, the<br>existence of EFX allocations has not been settled and is one of the most<br>important problems in fair division. Towards resolving this problem, many<br>impressive results show the existence of its relaxations, e.g., the existence<br>of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated<br>goods. The latter result was recently improved for three agents, in which the<br>two unallocated goods are allocated through an involved procedure. Reducing the<br>number of unallocated goods for arbitrary number of agents is a systematic way<br>to settle the big question. In this paper, we develop a new approach, and show<br>that for every $\varepsilon \in (0,1/2]$, there always exists a<br>$(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and<br>high Nash welfare.<br> For this, we reduce the EFX problem to a novel problem in extremal graph<br>theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d<br>\in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite<br>digraph $G =(\cup_{i \in [k]} V_i, E)$, in which<br> 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for<br>all $i \in [k]$,<br> 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming<br>edge from some vertex in $V_j$ and vice-versa, and<br> 3) there exists no cycle in $G$ that contains at most one vertex from each<br>part.<br> We show that any upper bound on $R(d)$ directly translates to a sublinear<br>bound on the number of unallocated goods. We establish a polynomial upper bound<br>on $R(d)$, yielding our main result. Furthermore, our approach is constructive,<br>which also gives a polynomial-time algorithm for finding such an allocation.<br>},
}

Endnote

%0 Report
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%A Mehta, Ruta
%A Misra, Pranabendu
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improving EFX Guarantees through Rainbow Cycle Number :
%G eng
%U http://hdl.handle.net/21.11116/0000-0008-DB40-9
%U https://arxiv.org/abs/2103.01628
%D 2021
%X We study the problem of fairly allocating a set of indivisible goods among<br>$n$ agents with additive valuations. Envy-freeness up to any good (EFX) is<br>arguably the most compelling fairness notion in this context. However, the<br>existence of EFX allocations has not been settled and is one of the most<br>important problems in fair division. Towards resolving this problem, many<br>impressive results show the existence of its relaxations, e.g., the existence<br>of $0.618$-EFX allocations, and the existence of EFX at most $n-1$ unallocated<br>goods. The latter result was recently improved for three agents, in which the<br>two unallocated goods are allocated through an involved procedure. Reducing the<br>number of unallocated goods for arbitrary number of agents is a systematic way<br>to settle the big question. In this paper, we develop a new approach, and show<br>that for every $\varepsilon \in (0,1/2]$, there always exists a<br>$(1-\varepsilon)$-EFX allocation with sublinear number of unallocated goods and<br>high Nash welfare.<br> For this, we reduce the EFX problem to a novel problem in extremal graph<br>theory. We introduce the notion of rainbow cycle number $R(\cdot)$. For all $d<br>\in \mathbb{N}$, $R(d)$ is the largest $k$ such that there exists a $k$-partite<br>digraph $G =(\cup_{i \in [k]} V_i, E)$, in which<br> 1) each part has at most $d$ vertices, i.e., $\lvert V_i \rvert \leq d$ for<br>all $i \in [k]$,<br> 2) for any two parts $V_i$ and $V_j$, each vertex in $V_i$ has an incoming<br>edge from some vertex in $V_j$ and vice-versa, and<br> 3) there exists no cycle in $G$ that contains at most one vertex from each<br>part.<br> We show that any upper bound on $R(d)$ directly translates to a sublinear<br>bound on the number of unallocated goods. We establish a polynomial upper bound<br>on $R(d)$, yielding our main result. Furthermore, our approach is constructive,<br>which also gives a polynomial-time algorithm for finding such an allocation.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Data Structures and Algorithms, cs.DS

[19]

B. Ray Chaudhury, T. Kavitha, K. Mehlhorn, and A. Sgouritsa, “A Little Charity Guarantees Almost Envy-Freeness,” SIAM Journal on Computing, vol. 50, no. 4, 2021.

Export

BibTeX

@article{RayChaudhury21,
TITLE = {A Little Charity Guarantees Almost Envy-Freeness},
AUTHOR = {Ray Chaudhury, Bhaskar and Kavitha, Telikepalli and Mehlhorn, Kurt and Sgouritsa, Alkmini},
LANGUAGE = {eng},
ISSN = {0097-5397},
DOI = {10.1137/20M1359134},
PUBLISHER = {SIAM},
ADDRESS = {Philadelphia, PA},
YEAR = {2021},
MARGINALMARK = {$\bullet$},
JOURNAL = {SIAM Journal on Computing},
VOLUME = {50},
NUMBER = {4},
PAGES = {1336--1358},
}

Endnote

%0 Journal Article
%A Ray Chaudhury, Bhaskar
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Sgouritsa, Alkmini
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T A Little Charity Guarantees Almost Envy-Freeness :
%G eng
%U http://hdl.handle.net/21.11116/0000-0009-2B38-9
%R 10.1137/20M1359134
%7 2021
%D 2021
%J SIAM Journal on Computing
%V 50
%N 4
%& 1336
%P 1336 - 1358
%I SIAM
%C Philadelphia, PA
%@ false

2020

[20]

V. Bonifaci, E. Facca, F. Folz, A. Karrenbauer, P. Kolev, K. Mehlhorn, G. Morigi, G. Shahkarami, and Q. Vermande, “Physarum Multi-Commodity Flow Dynamics,” 2020. [Online]. Available: https://arxiv.org/abs/2009.01498. (arXiv: 2009.01498)

Abstract

In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the<br>slime mold Physarum polycephalum has demonstrated its ability to solve shortest<br>path problems and to design efficient networks, see Figure \ref{Wet-Lab<br>Experiments} for illustrations. Physarum polycephalum is a slime mold in the<br>Mycetozoa group. For the shortest path problem, a mathematical model for the<br>evolution of the slime was proposed in \cite{Tero-Kobayashi-Nakagaki} and its<br>biological relevance was argued. The model was shown to solve shortest path<br>problems, first in computer simulations and then by mathematical proof. It was<br>later shown that the slime mold dynamics can solve more general linear programs<br>and that many variants of the dynamics have similar convergence behavior. In<br>this paper, we introduce a dynamics for the network design problem. We<br>formulate network design as the problem of constructing a network that<br>efficiently supports a multi-commodity flow problem. We investigate the<br>dynamics in computer simulations and analytically. The simulations show that<br>the dynamics is able to construct efficient and elegant networks. In the<br>theoretical part we show that the dynamics minimizes an objective combining the<br>cost of the network and the cost of routing the demands through the network. We<br>also give alternative characterization of the optimum solution.<br>

Export

BibTeX

@online{Bonifaci_arXiv2009.01498,
TITLE = {Physarum Multi-Commodity Flow Dynamics},
AUTHOR = {Bonifaci, Vincenzo and Facca, Enrico and Folz, Frederic and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt and Morigi, Giovanna and Shahkarami, Golnoosh and Vermande, Quentin},
LANGUAGE = {eng},
URL = {https://arxiv.org/abs/2009.01498},
EPRINT = {2009.01498},
EPRINTTYPE = {arXiv},
YEAR = {2020},
ABSTRACT = {In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the<br>slime mold Physarum polycephalum has demonstrated its ability to solve shortest<br>path problems and to design efficient networks, see Figure \ref{Wet-Lab<br>Experiments} for illustrations. Physarum polycephalum is a slime mold in the<br>Mycetozoa group. For the shortest path problem, a mathematical model for the<br>evolution of the slime was proposed in \cite{Tero-Kobayashi-Nakagaki} and its<br>biological relevance was argued. The model was shown to solve shortest path<br>problems, first in computer simulations and then by mathematical proof. It was<br>later shown that the slime mold dynamics can solve more general linear programs<br>and that many variants of the dynamics have similar convergence behavior. In<br>this paper, we introduce a dynamics for the network design problem. We<br>formulate network design as the problem of constructing a network that<br>efficiently supports a multi-commodity flow problem. We investigate the<br>dynamics in computer simulations and analytically. The simulations show that<br>the dynamics is able to construct efficient and elegant networks. In the<br>theoretical part we show that the dynamics minimizes an objective combining the<br>cost of the network and the cost of routing the demands through the network. We<br>also give alternative characterization of the optimum solution.<br>},
}

Endnote

%0 Report
%A Bonifaci, Vincenzo
%A Facca, Enrico
%A Folz, Frederic
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%A Morigi, Giovanna
%A Shahkarami, Golnoosh
%A Vermande, Quentin
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Physarum Multi-Commodity Flow Dynamics :
%G eng
%U http://hdl.handle.net/21.11116/0000-0007-2312-D
%U https://arxiv.org/abs/2009.01498
%D 2020
%X In wet-lab experiments \cite{Nakagaki-Yamada-Toth,Tero-Takagi-etal}, the<br>slime mold Physarum polycephalum has demonstrated its ability to solve shortest<br>path problems and to design efficient networks, see Figure \ref{Wet-Lab<br>Experiments} for illustrations. Physarum polycephalum is a slime mold in the<br>Mycetozoa group. For the shortest path problem, a mathematical model for the<br>evolution of the slime was proposed in \cite{Tero-Kobayashi-Nakagaki} and its<br>biological relevance was argued. The model was shown to solve shortest path<br>problems, first in computer simulations and then by mathematical proof. It was<br>later shown that the slime mold dynamics can solve more general linear programs<br>and that many variants of the dynamics have similar convergence behavior. In<br>this paper, we introduce a dynamics for the network design problem. We<br>formulate network design as the problem of constructing a network that<br>efficiently supports a multi-commodity flow problem. We investigate the<br>dynamics in computer simulations and analytically. The simulations show that<br>the dynamics is able to construct efficient and elegant networks. In the<br>theoretical part we show that the dynamics minimizes an objective combining the<br>cost of the network and the cost of routing the demands through the network. We<br>also give alternative characterization of the optimum solution.<br>
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Neural and Evolutionary Computing, cs.NE

[21]

E. Facca, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Directed Physarum Model,” Theoretical Computer Science, vol. 816, 2020.

Export

BibTeX

@article{FaccaTCS2020,
TITLE = {Convergence of the Non-Uniform Directed Physarum Model},
AUTHOR = {Facca, Enrico and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0304-3975},
DOI = {10.1016/j.tcs.2020.01.034},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2020},
DATE = {2020},
JOURNAL = {Theoretical Computer Science},
VOLUME = {816},
PAGES = {184--194},
}

Endnote

%0 Journal Article
%A Facca, Enrico
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Convergence of the Non-Uniform Directed Physarum Model :
%G eng
%U http://hdl.handle.net/21.11116/0000-0006-97B9-F
%R 10.1016/j.tcs.2020.01.034
%7 2020
%D 2020
%J Theoretical Computer Science
%V 816
%& 184
%P 184 - 194
%I Elsevier
%C Amsterdam
%@ false

[22]

D. Halperin, S. Har-Peled, K. Mehlhorn, E. Oh, and M. Sharir, “The Maximum-Level Vertex in an Arrangement of Lines,” 2020. [Online]. Available: http://arxiv.org/abs/2003.00518. (arXiv: 2003.00518)

Abstract

Let $L$ be a set of $n$ lines in the plane, not necessarily in general<br>position. We present an efficient algorithm for finding all the vertices of the<br>arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the<br>number of lines of $L$ that pass strictly below $v$. The problem, posed in<br>Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it<br>seems, as this vertex might not be on the upper envelope of the lines.<br> We first assume that all the lines of $L$ are distinct, and distinguish<br>between two cases, depending on whether or not the upper envelope of $L$<br>contains a bounded edge. In the former case, we show that the number of lines<br>of $L$ that pass above any maximum level vertex $v_0$ is only $O(\log n)$. In<br>the latter case, we establish a similar property that holds after we remove<br>some of the lines that are incident to the single vertex of the upper envelope.<br>We present algorithms that run, in both cases, in optimal $O(n\log n)$ time.<br> We then consider the case where the lines of $L$ are not necessarily<br>distinct. This setup is more challenging, and the best we have is an algorithm<br>that computes all the maximum-level vertices in time $O(n^{4/3}\log^{3}n)$.<br> Finally, we consider a related combinatorial question for degenerate<br>arrangements, where many lines may intersect in a single point, but all the<br>lines are distinct: We bound the complexity of the weighted $k$-level in such<br>an arrangement, where the weight of a vertex is the number of lines that pass<br>through the vertex. We show that the bound in this case is $O(n^{4/3})$, which<br>matches the corresponding bound for non-degenerate arrangements, and we use<br>this bound in the analysis of one of our algorithms.<br>

Export

BibTeX

@online{Halperin_arXiv2003.00518,
TITLE = {The Maximum-Level Vertex in an Arrangement of Lines},
AUTHOR = {Halperin, Dan and Har-Peled, Sariel and Mehlhorn, Kurt and Oh, Eunjin and Sharir, Micha},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/2003.00518},
EPRINT = {2003.00518},
EPRINTTYPE = {arXiv},
YEAR = {2020},
ABSTRACT = {Let $L$ be a set of $n$ lines in the plane, not necessarily in general<br>position. We present an efficient algorithm for finding all the vertices of the<br>arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the<br>number of lines of $L$ that pass strictly below $v$. The problem, posed in<br>Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it<br>seems, as this vertex might not be on the upper envelope of the lines.<br> We first assume that all the lines of $L$ are distinct, and distinguish<br>between two cases, depending on whether or not the upper envelope of $L$<br>contains a bounded edge. In the former case, we show that the number of lines<br>of $L$ that pass above any maximum level vertex $v_0$ is only $O(\log n)$. In<br>the latter case, we establish a similar property that holds after we remove<br>some of the lines that are incident to the single vertex of the upper envelope.<br>We present algorithms that run, in both cases, in optimal $O(n\log n)$ time.<br> We then consider the case where the lines of $L$ are not necessarily<br>distinct. This setup is more challenging, and the best we have is an algorithm<br>that computes all the maximum-level vertices in time $O(n^{4/3}\log^{3}n)$.<br> Finally, we consider a related combinatorial question for degenerate<br>arrangements, where many lines may intersect in a single point, but all the<br>lines are distinct: We bound the complexity of the weighted $k$-level in such<br>an arrangement, where the weight of a vertex is the number of lines that pass<br>through the vertex. We show that the bound in this case is $O(n^{4/3})$, which<br>matches the corresponding bound for non-degenerate arrangements, and we use<br>this bound in the analysis of one of our algorithms.<br>},
}

Endnote

%0 Report
%A Halperin, Dan
%A Har-Peled, Sariel
%A Mehlhorn, Kurt
%A Oh, Eunjin
%A Sharir, Micha
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T The Maximum-Level Vertex in an Arrangement of Lines :
%G eng
%U http://hdl.handle.net/21.11116/0000-0006-AFB1-D
%U http://arxiv.org/abs/2003.00518
%D 2020
%X Let $L$ be a set of $n$ lines in the plane, not necessarily in general<br>position. We present an efficient algorithm for finding all the vertices of the<br>arrangement $A(L)$ of maximum level, where the level of a vertex $v$ is the<br>number of lines of $L$ that pass strictly below $v$. The problem, posed in<br>Exercise~8.13 in de Berg etal [BCKO08], appears to be much harder than it<br>seems, as this vertex might not be on the upper envelope of the lines.<br> We first assume that all the lines of $L$ are distinct, and distinguish<br>between two cases, depending on whether or not the upper envelope of $L$<br>contains a bounded edge. In the former case, we show that the number of lines<br>of $L$ that pass above any maximum level vertex $v_0$ is only $O(\log n)$. In<br>the latter case, we establish a similar property that holds after we remove<br>some of the lines that are incident to the single vertex of the upper envelope.<br>We present algorithms that run, in both cases, in optimal $O(n\log n)$ time.<br> We then consider the case where the lines of $L$ are not necessarily<br>distinct. This setup is more challenging, and the best we have is an algorithm<br>that computes all the maximum-level vertices in time $O(n^{4/3}\log^{3}n)$.<br> Finally, we consider a related combinatorial question for degenerate<br>arrangements, where many lines may intersect in a single point, but all the<br>lines are distinct: We bound the complexity of the weighted $k$-level in such<br>an arrangement, where the weight of a vertex is the number of lines that pass<br>through the vertex. We show that the bound in this case is $O(n^{4/3})$, which<br>matches the corresponding bound for non-degenerate arrangements, and we use<br>this bound in the analysis of one of our algorithms.<br>
%K Computer Science, Computational Geometry, cs.CG

[23]

A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Physarum Dynamics,” Theoretical Computer Science, vol. 816, 2020.

Export

BibTeX

@article{KarrenbauerTCS2020,
TITLE = {Convergence of the Non-Uniform Physarum Dynamics},
AUTHOR = {Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0304-3975},
DOI = {10.1016/j.tcs.2020.02.032},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2020},
DATE = {2020},
JOURNAL = {Theoretical Computer Science},
VOLUME = {816},
PAGES = {260--269},
}

Endnote

%0 Journal Article
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Convergence of the Non-Uniform Physarum Dynamics :
%G eng
%U http://hdl.handle.net/21.11116/0000-0006-97C1-5
%R 10.1016/j.tcs.2020.02.032
%7 2020
%D 2020
%J Theoretical Computer Science
%V 816
%& 260
%P 260 - 269
%I Elsevier
%C Amsterdam
%@ false

[24]

B. Ray Chaudhury, J. Garg, and K. Mehlhorn, “EFX Exists for Three Agents,” in EC ’20, 21st ACM Conference on Economics and Computation, Virtual Event, Hungary, 2020.

Export

BibTeX

@inproceedings{RayChaudhury_EC2020,
TITLE = {{EFX} Exists for Three Agents},
AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-1-4503-7975-5},
DOI = {10.1145/3391403.3399511},
PUBLISHER = {ACM},
YEAR = {2020},
BOOKTITLE = {EC '20, 21st ACM Conference on Economics and Computation},
EDITOR = {Bir{\'o}, P{\'e}ter and Hartline, Jason},
PAGES = {1--19},
ADDRESS = {Virtual Event, Hungary},
}

Endnote

%0 Conference Proceedings
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T EFX Exists for Three Agents :
%G eng
%U http://hdl.handle.net/21.11116/0000-0007-223A-2
%R 10.1145/3391403.3399511
%D 2020
%B 21st ACM Conference on Economics and Computation
%Z date of event: 2020-07-13 - 2020-07-17
%C Virtual Event, Hungary
%B EC '20
%E Biró, Péter; Hartline, Jason
%P 1 - 19
%I ACM
%@ 978-1-4503-7975-5

[25]

B. Ray Chaudhury, J. Garg, and K. Mehlhorn, “EFX exists for three agents,” 2020. [Online]. Available: http://arxiv.org/abs/2002.05119. (arXiv: 2002.05119)

Abstract

We study the problem of distributing a set of indivisible items among agents<br>with additive valuations in a $\mathit{fair}$ manner. The fairness notion under<br>consideration is Envy-freeness up to any item (EFX). Despite significant<br>efforts by many researchers for several years, the existence of EFX allocations<br>has not been settled beyond the simple case of two agents. In this paper, we<br>show constructively that an EFX allocation always exists for three agents.<br>Furthermore, we falsify the conjecture by Caragiannis et al. by showing an<br>instance with three agents for which there is a partial EFX allocation (some<br>items are not allocated) with higher Nash welfare than that of any complete EFX<br>allocation.<br>

Export

BibTeX

@online{RayChaudhury_arXiv2002.05119,
TITLE = {{EFX} exists for three agents},
AUTHOR = {Ray Chaudhury, Bhaskar and Garg, Jugal and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/2002.05119},
EPRINT = {2002.05119},
EPRINTTYPE = {arXiv},
YEAR = {2020},
ABSTRACT = {We study the problem of distributing a set of indivisible items among agents<br>with additive valuations in a $\mathit{fair}$ manner. The fairness notion under<br>consideration is Envy-freeness up to any item (EFX). Despite significant<br>efforts by many researchers for several years, the existence of EFX allocations<br>has not been settled beyond the simple case of two agents. In this paper, we<br>show constructively that an EFX allocation always exists for three agents.<br>Furthermore, we falsify the conjecture by Caragiannis et al. by showing an<br>instance with three agents for which there is a partial EFX allocation (some<br>items are not allocated) with higher Nash welfare than that of any complete EFX<br>allocation.<br>},
}

Endnote

%0 Report
%A Ray Chaudhury, Bhaskar
%A Garg, Jugal
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T EFX exists for three agents :
%G eng
%U http://hdl.handle.net/21.11116/0000-0006-AF99-9
%U http://arxiv.org/abs/2002.05119
%D 2020
%X We study the problem of distributing a set of indivisible items among agents<br>with additive valuations in a $\mathit{fair}$ manner. The fairness notion under<br>consideration is Envy-freeness up to any item (EFX). Despite significant<br>efforts by many researchers for several years, the existence of EFX allocations<br>has not been settled beyond the simple case of two agents. In this paper, we<br>show constructively that an EFX allocation always exists for three agents.<br>Furthermore, we falsify the conjecture by Caragiannis et al. by showing an<br>instance with three agents for which there is a partial EFX allocation (some<br>items are not allocated) with higher Nash welfare than that of any complete EFX<br>allocation.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT,

[26]

B. Ray Chaudhury, T. Kavitha, K. Mehlhorn, and A. Sgouritsa, “A Little Charity Guarantees Almost Envy-Freeness,” in Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), Salt Lake City, UT, USA, 2020.

Export

BibTeX

@inproceedings{RayChaudhury_SODA20,
TITLE = {A Little Charity Guarantees Almost Envy-Freeness},
AUTHOR = {Ray Chaudhury, Bhaskar and Kavitha, Telikepalli and Mehlhorn, Kurt and Sgouritsa, Alkmini},
LANGUAGE = {eng},
ISBN = {978-1-61197-599-4},
DOI = {10.1137/1.9781611975994.162},
PUBLISHER = {SIAM},
YEAR = {2020},
BOOKTITLE = {Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms (SODA 2020)},
EDITOR = {Chawla, Shuchi},
PAGES = {2658 --2672},
ADDRESS = {Salt Lake City, UT, USA},
}

Endnote

%0 Conference Proceedings
%A Ray Chaudhury, Bhaskar
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Sgouritsa, Alkmini
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T A Little Charity Guarantees Almost Envy-Freeness :
%G eng
%U http://hdl.handle.net/21.11116/0000-0006-AF89-B
%R 10.1137/1.9781611975994.162
%D 2020
%B 31st Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2020-01-05 - 2020-01-08
%C Salt Lake City, UT, USA
%B Proceedings of the Thirty-First ACM-SIAM Symposium on Discrete Algorithms
%E Chawla, Shuchi
%P 2658 - 2672
%I SIAM
%@ 978-1-61197-599-4

2019

[27]

M. Abdulaziz, K. Mehlhorn, and T. Nipkow, “Trustworthy Graph Algorithms,” 2019. [Online]. Available: http://arxiv.org/abs/1907.04065. (arXiv: 1907.04065)

Abstract

The goal of the LEDA project was to build an easy-to-use and extendable<br>library of correct and efficient data structures, graph algorithms and<br>geometric algorithms. We report on the use of formal program verification to<br>achieve an even higher level of trustworthiness. Specifically, we report on an<br>ongoing and largely finished verification of the blossom-shrinking algorithm<br>for maximum cardinality matching.<br>

Export

BibTeX

@online{Abdulaziz_arXiv1907.04065,
TITLE = {Trustworthy Graph Algorithms},
AUTHOR = {Abdulaziz, Mohammad and Mehlhorn, Kurt and Nipkow, Tobias},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1907.04065},
EPRINT = {1907.04065},
EPRINTTYPE = {arXiv},
YEAR = {2019},
ABSTRACT = {The goal of the LEDA project was to build an easy-to-use and extendable<br>library of correct and efficient data structures, graph algorithms and<br>geometric algorithms. We report on the use of formal program verification to<br>achieve an even higher level of trustworthiness. Specifically, we report on an<br>ongoing and largely finished verification of the blossom-shrinking algorithm<br>for maximum cardinality matching.<br>},
}

Endnote

%0 Report
%A Abdulaziz, Mohammad
%A Mehlhorn, Kurt
%A Nipkow, Tobias
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Trustworthy Graph Algorithms :
%G eng
%U http://hdl.handle.net/21.11116/0000-0005-4FA8-6
%U http://arxiv.org/abs/1907.04065
%D 2019
%X The goal of the LEDA project was to build an easy-to-use and extendable<br>library of correct and efficient data structures, graph algorithms and<br>geometric algorithms. We report on the use of formal program verification to<br>achieve an even higher level of trustworthiness. Specifically, we report on an<br>ongoing and largely finished verification of the blossom-shrinking algorithm<br>for maximum cardinality matching.<br>
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Logic in Computer Science, cs.LO,Computer Science, Software Engineering, cs.SE

[28]

M. Abdulaziz, K. Mehlhorn, and T. Nipkow, “Trustworthy Graph Algorithms,” in 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019), Aachen, Germany, 2019.

Export

BibTeX

@inproceedings{Abdulaziz_MFCS,
TITLE = {Trustworthy Graph Algorithms},
AUTHOR = {Abdulaziz, Mohammad and Mehlhorn, Kurt and Nipkow, Tobias},
LANGUAGE = {eng},
ISSN = {1868-8969},
ISBN = {978-3-95977-117-7},
URL = {urn:nbn:de:0030-drops-109456},
DOI = {10.4230/LIPIcs.MFCS.2019.1},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2019},
BOOKTITLE = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
EDITOR = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
EID = {1},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {138},
ADDRESS = {Aachen, Germany},
}

Endnote

%0 Conference Proceedings
%A Abdulaziz, Mohammad
%A Mehlhorn, Kurt
%A Nipkow, Tobias
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Trustworthy Graph Algorithms :
%G eng
%U http://hdl.handle.net/21.11116/0000-0005-4F89-9
%R 10.4230/LIPIcs.MFCS.2019.1
%U urn:nbn:de:0030-drops-109456
%D 2019
%B 44th International Symposium on Mathematical Foundations of Computer Science
%Z date of event: 2019-08-26 - 2019-08-30
%C Aachen, Germany
%B 44th International Symposium on Mathematical Foundations of Computer Science
%E Rossmanith, Peter; Heggernes, Pinar; Katoen, Joost-Pieter
%Z sequence number: 1
%I Schloss Dagstuhl
%@ 978-3-95977-117-7
%B Leibniz International Proceedings in Informatics
%N 138
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2019/10945/http://drops.dagstuhl.de/doku/urheberrecht1.html

[29]

P. Afshani, M. Agrawal, B. Doerr, C. Doerr, K. G. Larsen, and K. Mehlhorn, “The Query Complexity of a Permutation-based Variant of Mastermind,” Discrete Applied Mathematics, vol. 260, 2019.

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BibTeX

@article{AFSHANI2019,
TITLE = {The query complexity of a permutation-based variant of {M}astermind},
AUTHOR = {Afshani, Peyman and Agrawal, Manindra and Doerr, Benjamin and Doerr, Carola and Larsen, Kasper Green and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0166-218X},
DOI = {10.1016/j.dam.2019.01.007},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {2019},
DATE = {2019},
JOURNAL = {Discrete Applied Mathematics},
VOLUME = {260},
PAGES = {28--50},
}

Endnote

%0 Journal Article
%A Afshani, Peyman
%A Agrawal, Manindra
%A Doerr, Benjamin
%A Doerr, Carola
%A Larsen, Kasper Green
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Query Complexity of a Permutation-based Variant of Mastermind :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-FE83-C
%R 10.1016/j.dam.2019.01.007
%7 2019
%D 2019
%J Discrete Applied Mathematics
%V 260
%& 28
%P 28 - 50
%I North-Holland
%C Amsterdam
%@ false

[30]

H. Akrami, K. Mehlhorn, and T. Odland, “Ratio-Balanced Maximum Flows,” 2019. [Online]. Available: http://arxiv.org/abs/1902.11047. (arXiv: 1902.11047)

Abstract

When a loan is approved for a person or company, the bank is subject to<br>\emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a<br>bank will require some form of \emph{security}, which will be collected if the<br>lender defaults. Accounts can be secured by several securities and a security<br>can be used for several accounts. The goal is to fractionally assign the<br>securities to the accounts so as to balance the risk.<br> This situation can be modelled by a bipartite graph. We have a set $S$ of<br>securities and a set $A$ of accounts. Each security has a \emph{value} $v_i$<br>and each account has an \emph{exposure} $e_j$. If a security $i$ can be used to<br>secure an account $j$, we have an edge from $i$ to $j$. Let $f_{ij}$ be part of<br>security $i$'s value used to secure account $j$. We are searching for a maximum<br>flow that send at most $v_i$ units out of node $i \in S$ and at most $e_j$<br>units into node $j \in A$. Then $s_j = e_j - \sum_i f_{ij}$ is the unsecured<br>part of account $j$. We are searching for the maximum flow that minimizes<br>$\sum_j s_j^2/e_j$.<br>

Export

BibTeX

@online{Akrami_arXiv1902.11047,
TITLE = {Ratio-Balanced Maximum Flows},
AUTHOR = {Akrami, Hannaneh and Mehlhorn, Kurt and Odland, Tommy},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1902.11047},
EPRINT = {1902.11047},
EPRINTTYPE = {arXiv},
YEAR = {2019},
ABSTRACT = {When a loan is approved for a person or company, the bank is subject to<br>\emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a<br>bank will require some form of \emph{security}, which will be collected if the<br>lender defaults. Accounts can be secured by several securities and a security<br>can be used for several accounts. The goal is to fractionally assign the<br>securities to the accounts so as to balance the risk.<br> This situation can be modelled by a bipartite graph. We have a set $S$ of<br>securities and a set $A$ of accounts. Each security has a \emph{value} $v_i$<br>and each account has an \emph{exposure} $e_j$. If a security $i$ can be used to<br>secure an account $j$, we have an edge from $i$ to $j$. Let $f_{ij}$ be part of<br>security $i$'s value used to secure account $j$. We are searching for a maximum<br>flow that send at most $v_i$ units out of node $i \in S$ and at most $e_j$<br>units into node $j \in A$. Then $s_j = e_j -- \sum_i f_{ij}$ is the unsecured<br>part of account $j$. We are searching for the maximum flow that minimizes<br>$\sum_j s_j^2/e_j$.<br>},
}

Endnote

%0 Report
%A Akrami, Hannaneh
%A Mehlhorn, Kurt
%A Odland, Tommy
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Ratio-Balanced Maximum Flows :
%G eng
%U http://hdl.handle.net/21.11116/0000-0003-B2FE-6
%U http://arxiv.org/abs/1902.11047
%D 2019
%X When a loan is approved for a person or company, the bank is subject to<br>\emph{credit risk}; the risk that the lender defaults. To mitigate this risk, a<br>bank will require some form of \emph{security}, which will be collected if the<br>lender defaults. Accounts can be secured by several securities and a security<br>can be used for several accounts. The goal is to fractionally assign the<br>securities to the accounts so as to balance the risk.<br> This situation can be modelled by a bipartite graph. We have a set $S$ of<br>securities and a set $A$ of accounts. Each security has a \emph{value} $v_i$<br>and each account has an \emph{exposure} $e_j$. If a security $i$ can be used to<br>secure an account $j$, we have an edge from $i$ to $j$. Let $f_{ij}$ be part of<br>security $i$'s value used to secure account $j$. We are searching for a maximum<br>flow that send at most $v_i$ units out of node $i \in S$ and at most $e_j$<br>units into node $j \in A$. Then $s_j = e_j - \sum_i f_{ij}$ is the unsecured<br>part of account $j$. We are searching for the maximum flow that minimizes<br>$\sum_j s_j^2/e_j$.<br>
%K Computer Science, Data Structures and Algorithms, cs.DS

[31]

H. Akrami, K. Mehlhorn, and T. Odland, “Ratio-Balanced Maximum Flows,” Information Processing Letters, vol. 150, 2019.

Export

BibTeX

@article{Akrami_2019,
TITLE = {Ratio-Balanced Maximum Flows},
AUTHOR = {Akrami, Hannaneh and Mehlhorn, Kurt and Odland, Tommy},
LANGUAGE = {eng},
ISSN = {0020-0190},
DOI = {10.1016/j.ipl.2019.06.003},
PUBLISHER = {Elsevier},
YEAR = {2019},
DATE = {2019},
JOURNAL = {Information Processing Letters},
VOLUME = {150},
PAGES = {13--17},
}

Endnote

%0 Journal Article
%A Akrami, Hannaneh
%A Mehlhorn, Kurt
%A Odland, Tommy
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Ratio-Balanced Maximum Flows :
%G eng
%U http://hdl.handle.net/21.11116/0000-0004-8FF0-C
%R 10.1016/j.ipl.2019.06.003
%7 2019
%D 2019
%J Information Processing Letters
%V 150
%& 13
%P 13 - 17
%I Elsevier
%@ false

[32]

R. Becker, V. Bonifaci, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Two Results on Slime Mold Computations,” Theoretical Computer Science, vol. 773, 2019.

Abstract

In this paper, we present two results on slime mold computations. The first<br>one treats a biologically-grounded model, originally proposed by biologists<br>analyzing the behavior of the slime mold Physarum polycephalum. This primitive<br>organism was empirically shown by Nakagaki et al. to solve shortest path<br>problems in wet-lab experiments (Nature'00). We show that the proposed simple<br>mathematical model actually generalizes to a much wider class of problems,<br>namely undirected linear programs with a non-negative cost vector.<br> For our second result, we consider the discretization of a<br>biologically-inspired model. This model is a directed variant of the<br>biologically-grounded one and was never claimed to describe the behavior of a<br>biological system. Straszak and Vishnoi showed that it can<br>$\epsilon$-approximately solve flow problems (SODA'16) and even general linear<br>programs with positive cost vector (ITCS'16) within a finite number of steps.<br>We give a refined convergence analysis that improves the dependence on<br>$\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a<br>step size that is independent of $\epsilon$. Furthermore, we show that the<br>dynamics can be initialized with a more general set of (infeasible) starting<br>points.<br>

Export

BibTeX

@article{BBKKM2018,
TITLE = {Two Results on Slime Mold Computations},
AUTHOR = {Becker, Ruben and Bonifaci, Vincenzo and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0304-3975},
DOI = {10.1016/j.tcs.2018.08.027},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2019},
DATE = {2019},
ABSTRACT = {In this paper, we present two results on slime mold computations. The first<br>one treats a biologically-grounded model, originally proposed by biologists<br>analyzing the behavior of the slime mold Physarum polycephalum. This primitive<br>organism was empirically shown by Nakagaki et al. to solve shortest path<br>problems in wet-lab experiments (Nature'00). We show that the proposed simple<br>mathematical model actually generalizes to a much wider class of problems,<br>namely undirected linear programs with a non-negative cost vector.<br> For our second result, we consider the discretization of a<br>biologically-inspired model. This model is a directed variant of the<br>biologically-grounded one and was never claimed to describe the behavior of a<br>biological system. Straszak and Vishnoi showed that it can<br>$\epsilon$-approximately solve flow problems (SODA'16) and even general linear<br>programs with positive cost vector (ITCS'16) within a finite number of steps.<br>We give a refined convergence analysis that improves the dependence on<br>$\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a<br>step size that is independent of $\epsilon$. Furthermore, we show that the<br>dynamics can be initialized with a more general set of (infeasible) starting<br>points.<br>},
JOURNAL = {Theoretical Computer Science},
VOLUME = {773},
PAGES = {79--106},
}

Endnote

%0 Journal Article
%A Becker, Ruben
%A Bonifaci, Vincenzo
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Two Results on Slime Mold Computations :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-A3AE-2
%R 10.1016/j.tcs.2018.08.027
%7 2018
%D 2019
%X In this paper, we present two results on slime mold computations. The first<br>one treats a biologically-grounded model, originally proposed by biologists<br>analyzing the behavior of the slime mold Physarum polycephalum. This primitive<br>organism was empirically shown by Nakagaki et al. to solve shortest path<br>problems in wet-lab experiments (Nature'00). We show that the proposed simple<br>mathematical model actually generalizes to a much wider class of problems,<br>namely undirected linear programs with a non-negative cost vector.<br> For our second result, we consider the discretization of a<br>biologically-inspired model. This model is a directed variant of the<br>biologically-grounded one and was never claimed to describe the behavior of a<br>biological system. Straszak and Vishnoi showed that it can<br>$\epsilon$-approximately solve flow problems (SODA'16) and even general linear<br>programs with positive cost vector (ITCS'16) within a finite number of steps.<br>We give a refined convergence analysis that improves the dependence on<br>$\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a<br>step size that is independent of $\epsilon$. Furthermore, we show that the<br>dynamics can be initialized with a more general set of (infeasible) starting<br>points.<br>
%K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Dynamical Systems, math.DS,Mathematics, Optimization and Control, math.OC, Physics, Biological Physics, physics.bio-ph
%J Theoretical Computer Science
%V 773
%& 79
%P 79 - 106
%I Elsevier
%C Amsterdam
%@ false

[33]

X. Bei, J. Garg, M. Hoefer, and K. Mehlhorn, “Earning and Utility Limits in Fisher Markets,” ACM Transactions on Economics and Computation, vol. 7, no. 2, 2019.

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BibTeX

@article{Bei2019,
TITLE = {Earning and Utility Limits in Fisher Markets},
AUTHOR = {Bei, Xiaohui and Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
DOI = {10.1145/3340234},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2019},
JOURNAL = {ACM Transactions on Economics and Computation},
VOLUME = {7},
NUMBER = {2},
EID = {10},
}

Endnote

%0 Journal Article
%A Bei, Xiaohui
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Earning and Utility Limits in Fisher Markets :
%G eng
%U http://hdl.handle.net/21.11116/0000-0005-4F7A-B
%R 10.1145/3340234
%7 2019
%D 2019
%J ACM Transactions on Economics and Computation
%O TEAC
%V 7
%N 2
%Z sequence number: 10
%I ACM
%C New York, NY

[34]

E. Facca, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Directed Physarum Model,” 2019. [Online]. Available: http://arxiv.org/abs/1906.07781. (arXiv: 1906.07781)

Abstract

The directed Physarum dynamics is known to solve positive linear programs:<br>minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector<br>$c$. The directed Physarum dynamics evolves a positive vector $x$ according to<br>the dynamics $\dot{x} = q(x) - x$. Here $q(x)$ is the solution to $Af = b$ that<br>minimizes the "energy" $\sum_i c_i f_i^2/x_i$.<br> In this paper, we study the non-uniform directed dynamics $\dot{x} = D(q(x) -<br>x)$, where $D$ is a positive diagonal matrix. The non-uniform dynamics is more<br>complex than the uniform dynamics (with $D$ being the identity matrix), as it<br>allows each component of $x$ to react with different speed to the differences<br>between $q(x)$ and $x$. Our contribution is to show that the non-uniform<br>directed dynamics solves positive linear programs.<br>

Export

BibTeX

@online{Facca_arXiv1906.07781,
TITLE = {Convergence of the Non-Uniform Directed Physarum Model},
AUTHOR = {Facca, Enrico and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1906.07781},
EPRINT = {1906.07781},
EPRINTTYPE = {arXiv},
YEAR = {2019},
ABSTRACT = {The directed Physarum dynamics is known to solve positive linear programs:<br>minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector<br>$c$. The directed Physarum dynamics evolves a positive vector $x$ according to<br>the dynamics $\dot{x} = q(x) -- x$. Here $q(x)$ is the solution to $Af = b$ that<br>minimizes the "energy" $\sum_i c_i f_i^2/x_i$.<br> In this paper, we study the non-uniform directed dynamics $\dot{x} = D(q(x) -<br>x)$, where $D$ is a positive diagonal matrix. The non-uniform dynamics is more<br>complex than the uniform dynamics (with $D$ being the identity matrix), as it<br>allows each component of $x$ to react with different speed to the differences<br>between $q(x)$ and $x$. Our contribution is to show that the non-uniform<br>directed dynamics solves positive linear programs.<br>},
}

Endnote

%0 Report
%A Facca, Enrico
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Convergence of the Non-Uniform Directed Physarum Model :
%G eng
%U http://hdl.handle.net/21.11116/0000-0005-1DBA-A
%U http://arxiv.org/abs/1906.07781
%D 2019
%X The directed Physarum dynamics is known to solve positive linear programs:<br>minimize $c^T x$ subject to $Ax = b$ and $x \ge 0$ for a positive cost vector<br>$c$. The directed Physarum dynamics evolves a positive vector $x$ according to<br>the dynamics $\dot{x} = q(x) - x$. Here $q(x)$ is the solution to $Af = b$ that<br>minimizes the "energy" $\sum_i c_i f_i^2/x_i$.<br> In this paper, we study the non-uniform directed dynamics $\dot{x} = D(q(x) -<br>x)$, where $D$ is a positive diagonal matrix. The non-uniform dynamics is more<br>complex than the uniform dynamics (with $D$ being the identity matrix), as it<br>allows each component of $x$ to react with different speed to the differences<br>between $q(x)$ and $x$. Our contribution is to show that the non-uniform<br>directed dynamics solves positive linear programs.<br>
%K Mathematics, Dynamical Systems, math.DS,Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Optimization and Control, math.OC

[35]

A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Convergence of the Non-Uniform Physarum Dynamics,” 2019. [Online]. Available: http://arxiv.org/abs/1901.07231. (arXiv: 1901.07231)

Abstract

Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in<br>\mathbb{Z}^n$. We show under fairly general conditions that the non-uniform<br>Physarum dynamics \[ \dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right) \] converges<br>to the optimum solution $x^*$ of the weighted basis pursuit problem minimize<br>$c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors<br>of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to<br>the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$,<br>and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| -<br>x_e$ at time $t$ and in state $x$. Previously convergence was only shown for<br>the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show<br>convergence for the dynamics \[ \dot{x}_e = x_e \cdot \left( g_e<br>\left(\frac{|q_e|}{x_e}\right) - 1\right),\] where $g_e$ is an increasing<br>differentiable function with $g_e(1) = 1$. Previously convergence was only<br>shown for the special case of the shortest path problem on a graph consisting<br>of two nodes connected by parallel edges.<br>

Export

BibTeX

@online{DBLP:journals/corr/abs-1901-07231,
TITLE = {Convergence of the Non-Uniform Physarum Dynamics},
AUTHOR = {Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1901.07231},
EPRINT = {1901.07231},
EPRINTTYPE = {arXiv},
YEAR = {2019},
ABSTRACT = {Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in<br>\mathbb{Z}^n$. We show under fairly general conditions that the non-uniform<br>Physarum dynamics \[ \dot{x}_e = a_e(x,t) \left(|q_e| -- x_e\right) \] converges<br>to the optimum solution $x^*$ of the weighted basis pursuit problem minimize<br>$c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors<br>of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to<br>the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$,<br>and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| -<br>x_e$ at time $t$ and in state $x$. Previously convergence was only shown for<br>the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show<br>convergence for the dynamics \[ \dot{x}_e = x_e \cdot \left( g_e<br>\left(\frac{|q_e|}{x_e}\right) -- 1\right),\] where $g_e$ is an increasing<br>differentiable function with $g_e(1) = 1$. Previously convergence was only<br>shown for the special case of the shortest path problem on a graph consisting<br>of two nodes connected by parallel edges.<br>},
}

Endnote

%0 Report
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Convergence of the Non-Uniform Physarum Dynamics :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-F39F-9
%U http://arxiv.org/abs/1901.07231
%D 2019
%X Let $c \in \mathbb{Z}^m_{> 0}$, $A \in \mathbb{Z}^{n\times m}$, and $b \in<br>\mathbb{Z}^n$. We show under fairly general conditions that the non-uniform<br>Physarum dynamics \[ \dot{x}_e = a_e(x,t) \left(|q_e| - x_e\right) \] converges<br>to the optimum solution $x^*$ of the weighted basis pursuit problem minimize<br>$c^T x$ subject to $A f = b$ and $|f| \le x$. Here, $f$ and $x$ are $m$-vectors<br>of real variables, $q$ minimizes the energy $\sum_e (c_e/x_e) q_e^2$ subject to<br>the constraints $A q = b$ and $\mathrm{supp}(q) \subseteq \mathrm{supp}(x)$,<br>and $a_e(x,t) > 0$ is the reactivity of edge $e$ to the difference $|q_e| -<br>x_e$ at time $t$ and in state $x$. Previously convergence was only shown for<br>the uniform case $a_e(x,t) = 1$ for all $e$, $x$, and $t$. We also show<br>convergence for the dynamics \[ \dot{x}_e = x_e \cdot \left( g_e<br>\left(\frac{|q_e|}{x_e}\right) - 1\right),\] where $g_e$ is an increasing<br>differentiable function with $g_e(1) = 1$. Previously convergence was only<br>shown for the special case of the shortest path problem on a graph consisting<br>of two nodes connected by parallel edges.<br>
%K Computer Science, Data Structures and Algorithms, cs.DS

[36]

B. Ray Chaudhury, T. Kavitha, K. Mehlhorn, and A. Sgouritsa, “A Little Charity Guarantees Almost Envy-Freeness,” 2019. [Online]. Available: http://arxiv.org/abs/1907.04596. (arXiv: 1907.04596)

Abstract

Fair division of indivisible goods is a very well-studied problem. The goal<br>of this problem is to distribute $m$ goods to $n$ agents in a "fair" manner,<br>where every agent has a valuation for each subset of goods. We assume general<br>valuations.<br> Envy-freeness is the most extensively studied notion of fairness. However,<br>envy-free allocations do not always exist when goods are indivisible. The<br>notion of fairness we consider here is "envy-freeness up to any good" (EFX)<br>where no agent envies another agent after the removal of any single good from<br>the other agent's bundle. It is not known if such an allocation always exists<br>even when $n=3$.<br> We show there is always a partition of the set of goods into $n+1$ subsets<br>$(X_1,\ldots,X_n,P)$ where for $i \in [n]$, $X_i$ is the bundle allocated to<br>agent $i$ and the set $P$ is unallocated (or donated to charity) such that we<br>have$\colon$<br> 1) envy-freeness up to any good,<br> 2) no agent values $P$ higher than her own bundle, and<br> 3) fewer than $n$ goods go to charity, i.e., $|P| < n$ (typically $m \gg n$).<br> Our proof is constructive. When agents have additive valuations and $\lvert P<br>\rvert$ is large (i.e., when $|P|$ is close to $n$), our allocation also has a<br>good maximin share (MMS) guarantee. Moreover, a minor variant of our algorithm<br>also shows the existence of an allocation which is $4/7$ groupwise maximin<br>share (GMMS): this is a notion of fairness stronger than MMS. This improves<br>upon the current best bound of $1/2$ known for an approximate GMMS allocation.<br>

Export

BibTeX

@online{Ray_arXiv1907.04596,
TITLE = {A Little Charity Guarantees Almost Envy-Freeness},
AUTHOR = {Ray Chaudhury, Bhaskar and Kavitha, Telikepalli and Mehlhorn, Kurt and Sgouritsa, Alkmini},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1907.04596},
EPRINT = {1907.04596},
EPRINTTYPE = {arXiv},
YEAR = {2019},
ABSTRACT = {Fair division of indivisible goods is a very well-studied problem. The goal<br>of this problem is to distribute $m$ goods to $n$ agents in a "fair" manner,<br>where every agent has a valuation for each subset of goods. We assume general<br>valuations.<br> Envy-freeness is the most extensively studied notion of fairness. However,<br>envy-free allocations do not always exist when goods are indivisible. The<br>notion of fairness we consider here is "envy-freeness up to any good" (EFX)<br>where no agent envies another agent after the removal of any single good from<br>the other agent's bundle. It is not known if such an allocation always exists<br>even when $n=3$.<br> We show there is always a partition of the set of goods into $n+1$ subsets<br>$(X_1,\ldots,X_n,P)$ where for $i \in [n]$, $X_i$ is the bundle allocated to<br>agent $i$ and the set $P$ is unallocated (or donated to charity) such that we<br>have$\colon$<br> 1) envy-freeness up to any good,<br> 2) no agent values $P$ higher than her own bundle, and<br> 3) fewer than $n$ goods go to charity, i.e., $|P| < n$ (typically $m \gg n$).<br> Our proof is constructive. When agents have additive valuations and $\lvert P<br>\rvert$ is large (i.e., when $|P|$ is close to $n$), our allocation also has a<br>good maximin share (MMS) guarantee. Moreover, a minor variant of our algorithm<br>also shows the existence of an allocation which is $4/7$ groupwise maximin<br>share (GMMS): this is a notion of fairness stronger than MMS. This improves<br>upon the current best bound of $1/2$ known for an approximate GMMS allocation.<br>},
}

Endnote

%0 Report
%A Ray Chaudhury, Bhaskar
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Sgouritsa, Alkmini
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Little Charity Guarantees Almost Envy-Freeness :
%G eng
%U http://hdl.handle.net/21.11116/0000-0005-4FB8-4
%U http://arxiv.org/abs/1907.04596
%D 2019
%X Fair division of indivisible goods is a very well-studied problem. The goal<br>of this problem is to distribute $m$ goods to $n$ agents in a "fair" manner,<br>where every agent has a valuation for each subset of goods. We assume general<br>valuations.<br> Envy-freeness is the most extensively studied notion of fairness. However,<br>envy-free allocations do not always exist when goods are indivisible. The<br>notion of fairness we consider here is "envy-freeness up to any good" (EFX)<br>where no agent envies another agent after the removal of any single good from<br>the other agent's bundle. It is not known if such an allocation always exists<br>even when $n=3$.<br> We show there is always a partition of the set of goods into $n+1$ subsets<br>$(X_1,\ldots,X_n,P)$ where for $i \in [n]$, $X_i$ is the bundle allocated to<br>agent $i$ and the set $P$ is unallocated (or donated to charity) such that we<br>have$\colon$<br> 1) envy-freeness up to any good,<br> 2) no agent values $P$ higher than her own bundle, and<br> 3) fewer than $n$ goods go to charity, i.e., $|P| < n$ (typically $m \gg n$).<br> Our proof is constructive. When agents have additive valuations and $\lvert P<br>\rvert$ is large (i.e., when $|P|$ is close to $n$), our allocation also has a<br>good maximin share (MMS) guarantee. Moreover, a minor variant of our algorithm<br>also shows the existence of an allocation which is $4/7$ groupwise maximin<br>share (GMMS): this is a notion of fairness stronger than MMS. This improves<br>upon the current best bound of $1/2$ known for an approximate GMMS allocation.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT

[37]

P. Sanders, K. Mehlhorn, M. Dietzfelbinger, and R. Dementiev, Sequential and Parallel Algorithms and Data Structures. Cham: Springer, 2019.

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BibTeX

@book{Sanders2019b,
TITLE = {Sequential and Parallel Algorithms and Data Structures},
AUTHOR = {Sanders, Peter and Mehlhorn, Kurt and Dietzfelbinger, Martin and Dementiev, Roman},
LANGUAGE = {eng},
ISBN = {978-3-030-25208-3; 978-3-030-25209-0},
DOI = {10.1007/978-3-030-25209-0},
PUBLISHER = {Springer},
ADDRESS = {Cham},
YEAR = {2019},
DATE = {2019},
PAGES = {434 p.},
}

Endnote

%0 Book
%A Sanders, Peter
%A Mehlhorn, Kurt
%A Dietzfelbinger, Martin
%A Dementiev, Roman
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Sequential and Parallel Algorithms and Data Structures : The Basic Toolbox
%G eng
%U http://hdl.handle.net/21.11116/0000-0005-3D79-0
%R 10.1007/978-3-030-25209-0
%@ 978-3-030-25208-3
%@ 978-3-030-25209-0
%I Springer
%C Cham
%D 2019
%P 434 p.

2018

[38]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Multi-Finger Binary Search Trees,” in 29th International Symposium on Algorithms and Computation (ISAAC 2018), Jiaoxi, Yilan, Taiwan, 2018.

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BibTeX

@inproceedings{Chalermsook_ISAAC2018b,
TITLE = {Multi-Finger Binary Search Trees},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, L{\`a}sz{\`o} and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
ISSN = {1868-8969},
ISBN = {978-3-95977-094-1},
URL = {urn:nbn:de:0030-drops-100032},
DOI = {10.4230/LIPIcs.ISAAC.2018.55},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2018},
BOOKTITLE = {29th International Symposium on Algorithms and Computation (ISAAC 2018)},
EDITOR = {Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
PAGES = {1--26},
EID = {55},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {123},
ADDRESS = {Jiaoxi, Yilan, Taiwan},
}

Endnote

%0 Conference Proceedings
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, Làszò
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Multi-Finger Binary Search Trees :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-AADE-5
%R 10.4230/LIPIcs.ISAAC.2018.55
%U urn:nbn:de:0030-drops-100032
%D 2018
%B 29th International Symposium on Algorithms and Computation
%Z date of event: 2018-12-16 - 2018-12-19
%C Jiaoxi, Yilan, Taiwan
%B 29th International Symposium on Algorithms and Computation
%E Hsu, Wen-Lian; Lee, Der-Tsai; Liao, Chung-Shou
%P 1 - 26
%Z sequence number: 55
%I Schloss Dagstuhl
%@ 978-3-95977-094-1
%B Leibniz International Proceedings in Informatics
%N 123
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2018/10003/http://drops.dagstuhl.de/doku/urheberrecht1.html

[39]

C. Croitoru and K. Mehlhorn, “On Testing Substitutability,” Information Processing Letters, vol. 138, 2018.

Export

BibTeX

@article{Croitoru_2018,
TITLE = {On Testing Substitutability},
AUTHOR = {Croitoru, Cosmina and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0020-0190},
DOI = {10.1016/j.ipl.2018.05.006},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2018},
DATE = {2018},
JOURNAL = {Information Processing Letters},
VOLUME = {138},
PAGES = {19--21},
}

Endnote

%0 Journal Article
%A Croitoru, Cosmina
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Testing Substitutability :
%G eng
%U http://hdl.handle.net/21.11116/0000-0001-EE14-D
%R 10.1016/j.ipl.2018.05.006
%7 2018
%D 2018
%J Information Processing Letters
%V 138
%& 19
%P 19 - 21
%I Elsevier
%C Amsterdam
%@ false

[40]

C. Croitoru and K. Mehlhorn, “On Testing Substitutability,” 2018. [Online]. Available: http://arxiv.org/abs/1805.07642. (arXiv: 1805.07642)

Abstract

The papers~\cite{hatfimmokomi11} and~\cite{azizbrilharr13} propose algorithms
for testing whether the choice function induced by a (strict) preference list
of length $N$ over a universe $U$ is substitutable. The running time of these
algorithms is $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this
note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that
$N$ may be exponential in the size $|U|$ of the universe.

Export

BibTeX

@online{Croitoru_arXiv1805.07642,
TITLE = {On Testing Substitutability},
AUTHOR = {Croitoru, Cosmina and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1805.07642},
EPRINT = {1805.07642},
EPRINTTYPE = {arXiv},
YEAR = {2018},
ABSTRACT = {The papers~\cite{hatfimmokomi11} and~\cite{azizbrilharr13} propose algorithms for testing whether the choice function induced by a (strict) preference list of length $N$ over a universe $U$ is substitutable. The running time of these algorithms is $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that $N$ may be exponential in the size $|U|$ of the universe.},
}

Endnote

%0 Report
%A Croitoru, Cosmina
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Testing Substitutability :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-05FA-F
%U http://arxiv.org/abs/1805.07642
%D 2018
%X The papers~\cite{hatfimmokomi11} and~\cite{azizbrilharr13} propose algorithms
for testing whether the choice function induced by a (strict) preference list
of length $N$ over a universe $U$ is substitutable. The running time of these
algorithms is $O(|U|^3\cdot N^3)$, respectively $O(|U|^2\cdot N^3)$. In this
note we present an algorithm with running time $O(|U|^2\cdot N^2)$. Note that
$N$ may be exponential in the size $|U|$ of the universe.
%K Computer Science, Data Structures and Algorithms, cs.DS,econ.EM

[41]

J. Garg, M. Hoefer, and K. Mehlhorn, “Approximating the Nash Social Welfare with Budget-Additive Valuations,” in Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018), New Orleans, LA, USA, 2018.

Export

BibTeX

@inproceedings{GargHoeferMehlhornSODA18,
TITLE = {Approximating the {Nash} Social Welfare with Budget-Additive Valuations},
AUTHOR = {Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-1-61197-503-1},
DOI = {10.1137/1.9781611975031.150},
PUBLISHER = {SIAM},
YEAR = {2018},
DATE = {2018},
BOOKTITLE = {Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2018)},
EDITOR = {Czumaj, Artur},
PAGES = {2326--2340},
ADDRESS = {New Orleans, LA, USA},
}

Endnote

%0 Conference Proceedings
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Approximating the Nash Social Welfare with Budget-Additive Valuations :
%G eng
%U http://hdl.handle.net/21.11116/0000-0000-37F9-A
%R 10.1137/1.9781611975031.150
%D 2018
%B Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2018-01-07 - 2018-01-10
%C New Orleans, LA, USA
%B Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
%E Czumaj, Artur
%P 2326 - 2340
%I SIAM
%@ 978-1-61197-503-1

[42]

P. Koprowski, K. Mehlhorn, and S. Ray, “Corrigendum to ‘Faster algorithms for computing Hong’s bound on absolute positiveness’ [J. Symb. Comput. 45 (2010) 677–683],” Journal of Symbolic Computation, vol. 87, 2018.

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BibTeX

@article{Koprowski2018,
TITLE = {Corrigendum to ``{F}aster algorithms for computing {H}ong's bound on absolute positiveness'' [{J. Symb. Comput.} 45 (2010) 677--683]},
AUTHOR = {Koprowski, Przemys{\l}aw and Mehlhorn, Kurt and Ray, Saurabh},
LANGUAGE = {eng},
ISSN = {0747-7171},
DOI = {10.1016/j.jsc.2017.05.008},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2018},
DATE = {2018},
JOURNAL = {Journal of Symbolic Computation},
VOLUME = {87},
PAGES = {238--241},
}

Endnote

%0 Journal Article
%A Koprowski, Przemysław
%A Mehlhorn, Kurt
%A Ray, Saurabh
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Corrigendum to “Faster algorithms for computing Hong's bound on absolute positiveness” [J. Symb. Comput. 45 (2010) 677–683] :
%G eng
%U http://hdl.handle.net/21.11116/0000-0001-3C55-D
%R 10.1016/j.jsc.2017.05.008
%7 2017
%D 2018
%J Journal of Symbolic Computation
%V 87
%& 238
%P 238 - 241
%I Elsevier
%C Amsterdam
%@ false

[43]

B. Ray Chaudhury, Y. K. Cheung, J. Garg, N. Garg, M. Hoefer, and K. Mehlhorn, “On Fair Division of Indivisible Items,” 2018. [Online]. Available: http://arxiv.org/abs/1805.06232. (arXiv: 1805.06232)

Abstract

We consider the task of assigning indivisible goods to a set of agents in a
fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is
to maximize the geometric mean of the utilities of the agents. Each good comes
in multiple items or copies, and the utility of an agent diminishes as it
receives more items of the same good. The utility of a bundle of items for an
agent is the sum of the utilities of the items in the bundle. Each agent has a
utility cap beyond which he does not value additional items. We give a
polynomial time approximation algorithm that maximizes Nash social welfare up
to a factor of $e^{1/e} \approx 1.445$.

Export

BibTeX

@online{Chaudhury_arXiv1805.06232,
TITLE = {On Fair Division of Indivisible Items},
AUTHOR = {Ray Chaudhury, Bhaskar and Cheung, Yun Kuen and Garg, Jugal and Garg, Naveen and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1805.06232},
EPRINT = {1805.06232},
EPRINTTYPE = {arXiv},
YEAR = {2018},
ABSTRACT = {We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of $e^{1/e} \approx 1.445$.},
}

Endnote

%0 Report
%A Ray Chaudhury, Bhaskar
%A Cheung, Yun Kuen
%A Garg, Jugal
%A Garg, Naveen
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Fair Division of Indivisible Items :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-05E7-4
%U http://arxiv.org/abs/1805.06232
%D 2018
%X We consider the task of assigning indivisible goods to a set of agents in a
fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is
to maximize the geometric mean of the utilities of the agents. Each good comes
in multiple items or copies, and the utility of an agent diminishes as it
receives more items of the same good. The utility of a bundle of items for an
agent is the sum of the utilities of the items in the bundle. Each agent has a
utility cap beyond which he does not value additional items. We give a
polynomial time approximation algorithm that maximizes Nash social welfare up
to a factor of $e^{1/e} \approx 1.445$.
%K Computer Science, Data Structures and Algorithms, cs.DS

[44]

B. Ray Chaudhury, Y. K. Cheung, J. Garg, N. Garg, M. Hoefer, and K. Mehlhorn, “On Fair Division for Indivisible Items,” in 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018), Ahmedabad, India, 2018.

Export

BibTeX

@inproceedings{Chaudhury_FSTTCS2018b,
TITLE = {On Fair Division for Indivisible Items},
AUTHOR = {Ray Chaudhury, Bhaskar and Cheung, Yun Kuen and Garg, Jugal and Garg, Naveen and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1868-896},
ISBN = {978-3-95977-093-4},
URL = {urn:nbn:de:0030-drops-99242},
DOI = {10.4230/LIPIcs.FSTTCS.2018.25},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2018},
BOOKTITLE = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
EDITOR = {Ganguly, Sumit and Pandya, Paritosh},
PAGES = {1--17},
EID = {25},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {122},
ADDRESS = {Ahmedabad, India},
}

Endnote

%0 Conference Proceedings
%A Ray Chaudhury, Bhaskar
%A Cheung, Yun Kuen
%A Garg, Jugal
%A Garg, Naveen
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Fair Division for Indivisible Items :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-AAE1-0
%R 10.4230/LIPIcs.FSTTCS.2018.25
%U urn:nbn:de:0030-drops-99242
%D 2018
%B 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
%Z date of event: 2018-12-11 - 2018-12-13
%C Ahmedabad, India
%B 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
%E Ganguly, Sumit; Pandya, Paritosh
%P 1 - 17
%Z sequence number: 25
%I Schloss Dagstuhl
%@ 978-3-95977-093-4
%B Leibniz International Proceedings in Informatics
%N 122
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2018/9924/http://drops.dagstuhl.de/doku/urheberrecht1.html

[45]

B. Ray Chaudhury and K. Mehlhorn, “Combinatorial Algorithms for General Linear Arrow-Debreu Markets,” 2018. [Online]. Available: http://arxiv.org/abs/1810.01237. (arXiv: 1810.01237)

Abstract

We present a combinatorial algorithm for determining the market clearing<br>prices of a general linear Arrow-Debreu market, where every agent can own<br>multiple goods. The existing combinatorial algorithms for linear Arrow-Debreu<br>markets consider the case where each agent can own all of one good only. We<br>present an $\tilde{\mathcal{O}}((n+m)^7 \log^3(UW))$ algorithm where $n$, $m$,<br>$U$ and $W$ refer to the number of agents, the number of goods, the maximal<br>integral utility and the maximum quantity of any good in the market<br>respectively. The algorithm refines the iterative algorithm of Duan, Garg and<br>Mehlhorn using several new ideas. We also identify the hard instances for<br>existing combinatorial algorithms for linear Arrow-Debreu markets. In<br>particular we find instances where the ratio of the maximum to the minimum<br>equilibrium price of a good is $U^{\Omega(n)}$ and the number of iterations<br>required by the existing iterative combinatorial algorithms of Duan, and<br>Mehlhorn and Duan, Garg, and Mehlhorn are high. Our instances also separate the<br>two algorithms.<br>

Export

BibTeX

@online{RayChaudhury_arxiv1810.01237,
TITLE = {Combinatorial Algorithms for General Linear {Arrow}-{Debreu} Markets},
AUTHOR = {Ray Chaudhury, Bhaskar and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1810.01237},
EPRINT = {1810.01237},
EPRINTTYPE = {arXiv},
YEAR = {2018},
ABSTRACT = {We present a combinatorial algorithm for determining the market clearing<br>prices of a general linear Arrow-Debreu market, where every agent can own<br>multiple goods. The existing combinatorial algorithms for linear Arrow-Debreu<br>markets consider the case where each agent can own all of one good only. We<br>present an $\tilde{\mathcal{O}}((n+m)^7 \log^3(UW))$ algorithm where $n$, $m$,<br>$U$ and $W$ refer to the number of agents, the number of goods, the maximal<br>integral utility and the maximum quantity of any good in the market<br>respectively. The algorithm refines the iterative algorithm of Duan, Garg and<br>Mehlhorn using several new ideas. We also identify the hard instances for<br>existing combinatorial algorithms for linear Arrow-Debreu markets. In<br>particular we find instances where the ratio of the maximum to the minimum<br>equilibrium price of a good is $U^{\Omega(n)}$ and the number of iterations<br>required by the existing iterative combinatorial algorithms of Duan, and<br>Mehlhorn and Duan, Garg, and Mehlhorn are high. Our instances also separate the<br>two algorithms.<br>},
}

Endnote

%0 Report
%A Ray Chaudhury, Bhaskar
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Combinatorial Algorithms for General Linear Arrow-Debreu Markets :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-57B5-0
%U http://arxiv.org/abs/1810.01237
%D 2018
%8 02.10.2018
%X We present a combinatorial algorithm for determining the market clearing<br>prices of a general linear Arrow-Debreu market, where every agent can own<br>multiple goods. The existing combinatorial algorithms for linear Arrow-Debreu<br>markets consider the case where each agent can own all of one good only. We<br>present an $\tilde{\mathcal{O}}((n+m)^7 \log^3(UW))$ algorithm where $n$, $m$,<br>$U$ and $W$ refer to the number of agents, the number of goods, the maximal<br>integral utility and the maximum quantity of any good in the market<br>respectively. The algorithm refines the iterative algorithm of Duan, Garg and<br>Mehlhorn using several new ideas. We also identify the hard instances for<br>existing combinatorial algorithms for linear Arrow-Debreu markets. In<br>particular we find instances where the ratio of the maximum to the minimum<br>equilibrium price of a good is $U^{\Omega(n)}$ and the number of iterations<br>required by the existing iterative combinatorial algorithms of Duan, and<br>Mehlhorn and Duan, Garg, and Mehlhorn are high. Our instances also separate the<br>two algorithms.<br>
%K Computer Science, Computer Science and Game Theory, cs.GT,

[46]

B. Ray Chaudhury and K. Mehlhorn, “Combinatorial Algorithms for General Linear Arrow-Debreu Markets,” in 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018), Ahmedabad, India, 2018.

Export

BibTeX

@inproceedings{Chaudhury_FSTTCS2018,
TITLE = {Combinatorial Algorithms for General Linear {A}rrow-{D}ebreu Markets},
AUTHOR = {Ray Chaudhury, Bhaskar and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1868-896},
ISBN = {978-3-95977-093-4},
URL = {urn:nbn:de:0030-drops-99255},
DOI = {10.4230/LIPIcs.FSTTCS.2018.26},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2018},
BOOKTITLE = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
EDITOR = {Ganguly, Sumit and Pandya, Paritosh},
PAGES = {1--16},
EID = {26},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {122},
ADDRESS = {Ahmedabad, India},
}

Endnote

%0 Conference Proceedings
%A Ray Chaudhury, Bhaskar
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Combinatorial Algorithms for General Linear Arrow-Debreu Markets :
%G eng
%U http://hdl.handle.net/21.11116/0000-0002-AADC-7
%R 10.4230/LIPIcs.FSTTCS.2018.26
%U urn:nbn:de:0030-drops-99255
%D 2018
%B 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
%Z date of event: 2018-12-11 - 2018-12-13
%C Ahmedabad, India
%B 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
%E Ganguly, Sumit; Pandya, Paritosh
%P 1 - 16
%Z sequence number: 26
%I Schloss Dagstuhl
%@ 978-3-95977-093-4
%B Leibniz International Proceedings in Informatics
%N 122
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2018/9925/http://drops.dagstuhl.de/doku/urheberrecht1.html

2017

[47]

R. Becker, V. Bonifaci, A. Karrenbauer, P. Kolev, and K. Mehlhorn, “Two Results on Slime Mold Computations,” 2017. [Online]. Available: http://arxiv.org/abs/1707.06631. (arXiv: 1707.06631)

Abstract

In this paper, we present two results on slime mold computations. The first
one treats a biologically-grounded model, originally proposed by biologists
analyzing the behavior of the slime mold Physarum polycephalum. This primitive
organism was empirically shown by Nakagaki et al. to solve shortest path
problems in wet-lab experiments (Nature'00). We show that the proposed simple
mathematical model actually generalizes to a much wider class of problems,
namely undirected linear programs with a non-negative cost vector.
For our second result, we consider the discretization of a
biologically-inspired model. This model is a directed variant of the
biologically-grounded one and was never claimed to describe the behavior of a
biological system. Straszak and Vishnoi showed that it can
$\epsilon$-approximately solve flow problems (SODA'16) and even general linear
programs with positive cost vector (ITCS'16) within a finite number of steps.
We give a refined convergence analysis that improves the dependence on
$\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a
step size that is independent of $\epsilon$. Furthermore, we show that the
dynamics can be initialized with a more general set of (infeasible) starting
points.

Export

BibTeX

@online{Becker_arxiv2017,
TITLE = {Two Results on Slime Mold Computations},
AUTHOR = {Becker, Ruben and Bonifaci, Vincenzo and Karrenbauer, Andreas and Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1707.06631},
EPRINT = {1707.06631},
EPRINTTYPE = {arXiv},
YEAR = {2017},
ABSTRACT = {In this paper, we present two results on slime mold computations. The first one treats a biologically-grounded model, originally proposed by biologists analyzing the behavior of the slime mold Physarum polycephalum. This primitive organism was empirically shown by Nakagaki et al. to solve shortest path problems in wet-lab experiments (Nature'00). We show that the proposed simple mathematical model actually generalizes to a much wider class of problems, namely undirected linear programs with a non-negative cost vector. For our second result, we consider the discretization of a biologically-inspired model. This model is a directed variant of the biologically-grounded one and was never claimed to describe the behavior of a biological system. Straszak and Vishnoi showed that it can $\epsilon$-approximately solve flow problems (SODA'16) and even general linear programs with positive cost vector (ITCS'16) within a finite number of steps. We give a refined convergence analysis that improves the dependence on $\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a step size that is independent of $\epsilon$. Furthermore, we show that the dynamics can be initialized with a more general set of (infeasible) starting points.},
}

Endnote

%0 Report
%A Becker, Ruben
%A Bonifaci, Vincenzo
%A Karrenbauer, Andreas
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Two Results on Slime Mold Computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002D-FBA8-F
%U http://arxiv.org/abs/1707.06631
%D 2017
%X In this paper, we present two results on slime mold computations. The first
one treats a biologically-grounded model, originally proposed by biologists
analyzing the behavior of the slime mold Physarum polycephalum. This primitive
organism was empirically shown by Nakagaki et al. to solve shortest path
problems in wet-lab experiments (Nature'00). We show that the proposed simple
mathematical model actually generalizes to a much wider class of problems,
namely undirected linear programs with a non-negative cost vector.
For our second result, we consider the discretization of a
biologically-inspired model. This model is a directed variant of the
biologically-grounded one and was never claimed to describe the behavior of a
biological system. Straszak and Vishnoi showed that it can
$\epsilon$-approximately solve flow problems (SODA'16) and even general linear
programs with positive cost vector (ITCS'16) within a finite number of steps.
We give a refined convergence analysis that improves the dependence on
$\epsilon$ from polynomial to logarithmic and simultaneously allows to choose a
step size that is independent of $\epsilon$. Furthermore, we show that the
dynamics can be initialized with a more general set of (infeasible) starting
points.
%K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Dynamical Systems, math.DS,Mathematics, Optimization and Control, math.OC, Physics, Biological Physics, physics.bio-ph

[48]

X. Bei, J. Garg, M. Hoefer, and K. Mehlhorn, “Earning Limits in Fisher Markets with Spending-Constraint Utilities,” in Algorithmic Game Theory (SAGT 2017), L’Aquila, Italy, 2017.

Export

BibTeX

@inproceedings{BeiSAGT2017,
TITLE = {Earning Limits in {Fisher} Markets with Spending-Constraint Utilities},
AUTHOR = {Bei, Xiaohui and Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-319-66699-0},
DOI = {10.1007/978-3-319-66700-3_6},
PUBLISHER = {Springer},
YEAR = {2017},
DATE = {2017},
BOOKTITLE = {Algorithmic Game Theory (SAGT 2017)},
PAGES = {67--79},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {10504},
ADDRESS = {L'Aquila, Italy},
}

Endnote

%0 Conference Proceedings
%A Bei, Xiaohui
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Earning Limits in Fisher Markets with Spending-Constraint Utilities :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002D-E7DB-7
%R 10.1007/978-3-319-66700-3_6
%D 2017
%B 10th International Symposium on Algorithmic Game Theory
%Z date of event: 2017-09-12 - 2017-09-14
%C L'Aquila, Italy
%B Algorithmic Game Theory
%P 67 - 79
%I Springer
%@ 978-3-319-66699-0
%B Lecture Notes in Computer Science
%N 10504

[49]

M. Dirnberger and K. Mehlhorn, “Characterizing Networks Formed by P. Polycephalum,” Journal of Physics D: Applied Physics, vol. 50, no. 22, 2017.

Export

BibTeX

@article{Dirnberg_Mehlhorn2017,
TITLE = {Characterizing networks formed by \textsl{P. polycephalum}},
AUTHOR = {Dirnberger, Michael and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0022-3727},
DOI = {10.1088/1361-6463/aa6e7b},
PUBLISHER = {IOP Publishing},
ADDRESS = {Bristol},
YEAR = {2017},
DATE = {2017},
JOURNAL = {Journal of Physics D: Applied Physics},
VOLUME = {50},
NUMBER = {22},
EID = {224002},
}

Endnote

%0 Journal Article
%A Dirnberger, Michael
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Characterizing Networks Formed by P. Polycephalum :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002D-56FA-2
%R 10.1088/1361-6463/aa6e7b
%7 2017
%D 2017
%J Journal of Physics D: Applied Physics
%O J. Phys. D: Appl. Phys.
%V 50
%N 22
%Z sequence number: 224002
%I IOP Publishing
%C Bristol
%@ false

[50]

M. Dirnberger, K. Mehlhorn, and T. Mehlhorn, “Introducing the Slime Mold Graph Repository,” Journal of Physics D: Applied Physics, vol. 50, no. 26, 2017.

Export

BibTeX

@article{Dirnberger2017,
TITLE = {Introducing the Slime Mold Graph Repository},
AUTHOR = {Dirnberger, Michael and Mehlhorn, Kurt and Mehlhorn, Tim},
LANGUAGE = {eng},
ISSN = {0022-3727},
DOI = {10.1088/1361-6463/aa7326},
PUBLISHER = {IOP Publishing},
ADDRESS = {Bristol},
YEAR = {2017},
DATE = {2017},
JOURNAL = {Journal of Physics D: Applied Physics},
VOLUME = {50},
NUMBER = {26},
EID = {264001},
}

Endnote

%0 Journal Article
%A Dirnberger, Michael
%A Mehlhorn, Kurt
%A Mehlhorn, Tim
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Introducing the Slime Mold Graph Repository :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002D-8464-B
%R 10.1088/1361-6463/aa7326
%7 2017
%D 2017
%J Journal of Physics D: Applied Physics
%O J. Phys. D: Appl. Phys.
%V 50
%N 26
%Z sequence number: 264001
%I IOP Publishing
%C Bristol
%@ false

[51]

J. Garg, M. Hoefer, and K. Mehlhorn, “Approximating the Nash Social Welfare with Budget-Additive Valuations,” 2017. [Online]. Available: http://arxiv.org/abs/1707.04428. (arXiv: 1707.04428)

Abstract

We present the first constant-factor approximation algorithm for maximizing
the Nash social welfare when allocating indivisible items to agents with
budget-additive valuation functions. Budget-additive valuations represent an
important class of submodular functions. They have attracted a lot of research
interest in recent years due to many interesting applications. For every
$\varepsilon > 0$, our algorithm obtains a $(2.404 +
\varepsilon)$-approximation in time polynomial in the input size and
$1/\varepsilon$.
Our algorithm relies on rounding an approximate equilibrium in a linear
Fisher market where sellers have earning limits (upper bounds on the amount of
money they want to earn) and buyers have utility limits (upper bounds on the
amount of utility they want to achieve). In contrast to markets with either
earning or utility limits, these markets have not been studied before. They
turn out to have fundamentally different properties.
Although the existence of equilibria is not guaranteed, we show that the
market instances arising from the Nash social welfare problem always have an
equilibrium. Further, we show that the set of equilibria is not convex,
answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an
approximate equilibrium, a result that may be of independent interest.

Export

BibTeX

@online{GargHoeferMehlhorn2017,
TITLE = {Approximating the {Nash} Social Welfare with Budget-Additive Valuations},
AUTHOR = {Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1707.04428},
EPRINT = {1707.04428},
EPRINTTYPE = {arXiv},
YEAR = {2017},
ABSTRACT = {We present the first constant-factor approximation algorithm for maximizing the Nash social welfare when allocating indivisible items to agents with budget-additive valuation functions. Budget-additive valuations represent an important class of submodular functions. They have attracted a lot of research interest in recent years due to many interesting applications. For every $\varepsilon > 0$, our algorithm obtains a $(2.404 + \varepsilon)$-approximation in time polynomial in the input size and $1/\varepsilon$. Our algorithm relies on rounding an approximate equilibrium in a linear Fisher market where sellers have earning limits (upper bounds on the amount of money they want to earn) and buyers have utility limits (upper bounds on the amount of utility they want to achieve). In contrast to markets with either earning or utility limits, these markets have not been studied before. They turn out to have fundamentally different properties. Although the existence of equilibria is not guaranteed, we show that the market instances arising from the Nash social welfare problem always have an equilibrium. Further, we show that the set of equilibria is not convex, answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an approximate equilibrium, a result that may be of independent interest.},
}

Endnote

%0 Report
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Approximating the Nash Social Welfare with Budget-Additive Valuations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002D-E7D6-2
%U http://arxiv.org/abs/1707.04428
%D 2017
%X We present the first constant-factor approximation algorithm for maximizing
the Nash social welfare when allocating indivisible items to agents with
budget-additive valuation functions. Budget-additive valuations represent an
important class of submodular functions. They have attracted a lot of research
interest in recent years due to many interesting applications. For every
$\varepsilon > 0$, our algorithm obtains a $(2.404 +
\varepsilon)$-approximation in time polynomial in the input size and
$1/\varepsilon$.
Our algorithm relies on rounding an approximate equilibrium in a linear
Fisher market where sellers have earning limits (upper bounds on the amount of
money they want to earn) and buyers have utility limits (upper bounds on the
amount of utility they want to achieve). In contrast to markets with either
earning or utility limits, these markets have not been studied before. They
turn out to have fundamentally different properties.
Although the existence of equilibria is not guaranteed, we show that the
market instances arising from the Nash social welfare problem always have an
equilibrium. Further, we show that the set of equilibria is not convex,
answering a question of [Cole et al, EC 2017]. We design an FPTAS to compute an
approximate equilibrium, a result that may be of independent interest.
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computer Science and Game Theory, cs.GT

[52]

K. Mehlhorn, A. Neumann, and J. M. Schmidt, “Certifying 3-Edge-Connectivity,” Algorithmica, vol. 77, no. 2, 2017.

Export

BibTeX

@article{Mehlhorn_Neumann_Schmidt2017,
TITLE = {Certifying 3-Edge-Connectivity},
AUTHOR = {Mehlhorn, Kurt and Neumann, Adrian and Schmidt, Jens M.},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-015-0075-x},
PUBLISHER = {Springer},
ADDRESS = {New York, NY, USA},
YEAR = {2017},
DATE = {2017},
JOURNAL = {Algorithmica},
VOLUME = {77},
NUMBER = {2},
PAGES = {309--335},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Neumann, Adrian
%A Schmidt, Jens M.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying 3-Edge-Connectivity :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002C-6971-B
%R 10.1007/s00453-015-0075-x
%7 2015-09-22
%D 2017
%J Algorithmica
%V 77
%N 2
%& 309
%P 309 - 335
%I Springer
%C New York, NY, USA
%@ false

[53]

K. Mehlhorn, S. Näher, and P. Sanders, “Engineering DFS-Based Graph Algorithms,” 2017. [Online]. Available: http://arxiv.org/abs/1703.10023. (arXiv: 1703.10023)

Export

BibTeX

@online{MehlhornDFSarXiv2017,
TITLE = {Engineering {DFS}-Based Graph Algorithms},
AUTHOR = {Mehlhorn, Kurt and N{\"a}her, Stefan and Sanders, Peter},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1703.10023},
EPRINT = {1703.10023},
EPRINTTYPE = {arXiv},
YEAR = {2017},
}

Endnote

%0 Report
%A Mehlhorn, Kurt
%A Näher, Stefan
%A Sanders, Peter
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Engineering DFS-Based Graph Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002B-4DAE-7
%U http://arxiv.org/abs/1703.10023
%D 2017

2016

[54]

R. Becker, A. Karrenbauer, and K. Mehlhorn, “An Integer Interior Point Method for Min-Cost Flow Using Arc Contractions and Deletions,” 2016. [Online]. Available: http://arxiv.org/abs/1612.04689. (arXiv: 1612.04689)

Abstract

We present an interior point method for the min-cost flow problem that uses
arc contractions and deletions to steer clear from the boundary of the polytope
when path-following methods come too close. We obtain a randomized algorithm
running in expected $\tilde O( m^{3/2} )$ time that only visits integer lattice
points in the vicinity of the central path of the polytope. This enables us to
use integer arithmetic like classical combinatorial algorithms typically do. We
provide explicit bounds on the size of the numbers that appear during all
computations. By presenting an integer arithmetic interior point algorithm we
avoid the tediousness of floating point error analysis and achieve a method
that is guaranteed to be free of any numerical issues. We thereby eliminate one
of the drawbacks of numerical methods in contrast to combinatorial min-cost
flow algorithms that still yield the most efficient implementations in
practice, despite their inferior worst-case time complexity.

Export

BibTeX

@online{DBLP:journals/corr/BeckerKM16,
TITLE = {An Integer Interior Point Method for Min-Cost Flow Using Arc Contractions and Deletions},
AUTHOR = {Becker, Ruben and Karrenbauer, Andreas and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1612.04689},
EPRINT = {1612.04689},
EPRINTTYPE = {arXiv},
YEAR = {2016},
ABSTRACT = {We present an interior point method for the min-cost flow problem that uses arc contractions and deletions to steer clear from the boundary of the polytope when path-following methods come too close. We obtain a randomized algorithm running in expected $\tilde O( m^{3/2} )$ time that only visits integer lattice points in the vicinity of the central path of the polytope. This enables us to use integer arithmetic like classical combinatorial algorithms typically do. We provide explicit bounds on the size of the numbers that appear during all computations. By presenting an integer arithmetic interior point algorithm we avoid the tediousness of floating point error analysis and achieve a method that is guaranteed to be free of any numerical issues. We thereby eliminate one of the drawbacks of numerical methods in contrast to combinatorial min-cost flow algorithms that still yield the most efficient implementations in practice, despite their inferior worst-case time complexity.},
}

Endnote

%0 Report
%A Becker, Ruben
%A Karrenbauer, Andreas
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T An Integer Interior Point Method for Min-Cost Flow Using Arc
Contractions and Deletions :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002C-5714-E
%U http://arxiv.org/abs/1612.04689
%D 2016
%X We present an interior point method for the min-cost flow problem that uses
arc contractions and deletions to steer clear from the boundary of the polytope
when path-following methods come too close. We obtain a randomized algorithm
running in expected $\tilde O( m^{3/2} )$ time that only visits integer lattice
points in the vicinity of the central path of the polytope. This enables us to
use integer arithmetic like classical combinatorial algorithms typically do. We
provide explicit bounds on the size of the numbers that appear during all
computations. By presenting an integer arithmetic interior point algorithm we
avoid the tediousness of floating point error analysis and achieve a method
that is guaranteed to be free of any numerical issues. We thereby eliminate one
of the drawbacks of numerical methods in contrast to combinatorial min-cost
flow algorithms that still yield the most efficient implementations in
practice, despite their inferior worst-case time complexity.
%K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Numerical Analysis, math.NA,Mathematics, Optimization and Control, math.OC

[55]

X. Bei, J. Garg, M. Hoefer, and K. Mehlhorn, “Computing Equilibria in Markets with Budget-Additive Utilities,” in 24th Annual European Symposium on Algorithms (ESA 2016), Aarhus, Denmark, 2016.

Export

BibTeX

@inproceedings{BeiESA2016,
TITLE = {Computing Equilibria in Markets with Budget-Additive Utilities},
AUTHOR = {Bei, Xiaohui and Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-95977-015-6},
URL = {urn:nbn:de:0030-drops-63504},
DOI = {10.4230/LIPIcs.ESA.2016.8},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2016},
BOOKTITLE = {24th Annual European Symposium on Algorithms (ESA 2016)},
EDITOR = {Sankowski, Piotr and Zaroliagis, Christos},
PAGES = {1--14},
EID = {8},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {57},
ADDRESS = {Aarhus, Denmark},
}

Endnote

%0 Conference Proceedings
%A Bei, Xiaohui
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Computing Equilibria in Markets with Budget-Additive Utilities :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002B-479B-5
%R 10.4230/LIPIcs.ESA.2016.8
%U urn:nbn:de:0030-drops-63504
%D 2016
%B 24th Annual European Symposium on Algorithms
%Z date of event: 2016-08-22 - 2016-08-26
%C Aarhus, Denmark
%B 24th Annual European Symposium on Algorithms
%E Sankowski, Piotr; Zaroliagis, Christos
%P 1 - 14
%Z sequence number: 8
%I Schloss Dagstuhl
%@ 978-3-95977-015-6
%B Leibniz International Proceedings in Informatics
%N 57
%U http://drops.dagstuhl.de/opus/volltexte/2016/6350/http://drops.dagstuhl.de/doku/urheberrecht1.html

[56]

X. Bei, J. Garg, M. Hoefer, and K. Mehlhorn, “Computing Equilibria in Markets with Budget-Additive Utilities,” 2016. [Online]. Available: http://arxiv.org/abs/1603.07210. (arXiv: 1603.07210)

Abstract

We present the first analysis of Fisher markets with buyers that have
budget-additive utility functions. Budget-additive utilities are elementary
concave functions with numerous applications in online adword markets and
revenue optimization problems. They extend the standard case of linear
utilities and have been studied in a variety of other market models. In
contrast to the frequently studied CES utilities, they have a global satiation
point which can imply multiple market equilibria with quite different
characteristics. Our main result is an efficient combinatorial algorithm to
compute a market equilibrium with a Pareto-optimal allocation of goods. It
relies on a new descending-price approach and, as a special case, also implies
a novel combinatorial algorithm for computing a market equilibrium in linear
Fisher markets. We complement these positive results with a number of hardness
results for related computational questions. We prove that it is NP-hard to
compute a market equilibrium that maximizes social welfare, and it is PPAD-hard
to find any market equilibrium with utility functions with separate satiation
points for each buyer and each good.

Export

BibTeX

@online{BeiGargHoeferMehlhorn2016,
TITLE = {Computing Equilibria in Markets with Budget-Additive Utilities},
AUTHOR = {Bei, Xiaohui and Garg, Jugal and Hoefer, Martin and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1603.07210},
EPRINT = {1603.07210},
EPRINTTYPE = {arXiv},
YEAR = {2016},
ABSTRACT = {We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a market equilibrium with a Pareto-optimal allocation of goods. It relies on a new descending-price approach and, as a special case, also implies a novel combinatorial algorithm for computing a market equilibrium in linear Fisher markets. We complement these positive results with a number of hardness results for related computational questions. We prove that it is NP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good.},
}

Endnote

%0 Report
%A Bei, Xiaohui
%A Garg, Jugal
%A Hoefer, Martin
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Computing Equilibria in Markets with Budget-Additive Utilities :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-FCC0-C
%U http://arxiv.org/abs/1603.07210
%D 2016
%X We present the first analysis of Fisher markets with buyers that have
budget-additive utility functions. Budget-additive utilities are elementary
concave functions with numerous applications in online adword markets and
revenue optimization problems. They extend the standard case of linear
utilities and have been studied in a variety of other market models. In
contrast to the frequently studied CES utilities, they have a global satiation
point which can imply multiple market equilibria with quite different
characteristics. Our main result is an efficient combinatorial algorithm to
compute a market equilibrium with a Pareto-optimal allocation of goods. It
relies on a new descending-price approach and, as a special case, also implies
a novel combinatorial algorithm for computing a market equilibrium in linear
Fisher markets. We complement these positive results with a number of hardness
results for related computational questions. We prove that it is NP-hard to
compute a market equilibrium that maximizes social welfare, and it is PPAD-hard
to find any market equilibrium with utility functions with separate satiation
points for each buyer and each good.
%K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Data Structures and Algorithms, cs.DS

[57]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “The Landscape of Bounds for Binary Search Trees,” 2016. [Online]. Available: http://arxiv.org/abs/1603.04892. (arXiv: 1603.04892)

Abstract

Binary search trees (BSTs) with rotations can adapt to various kinds of
structure in search sequences, achieving amortized access times substantially
better than the Theta(log n) worst-case guarantee. Classical examples of
structural properties include static optimality, sequential access, working
set, key-independent optimality, and dynamic finger, all of which are now known
to be achieved by the two famous online BST algorithms (Splay and Greedy).
(...)
In this paper, we introduce novel properties that explain the efficiency of
sequences not captured by any of the previously known properties, and which
provide new barriers to the dynamic optimality conjecture. We also establish
connections between various properties, old and new. For instance, we show the
following.
(i) A tight bound of O(n log d) on the cost of Greedy for d-decomposable
sequences. The result builds on the recent lazy finger result of Iacono and
Langerman (SODA 2016). On the other hand, we show that lazy finger alone cannot
explain the efficiency of pattern avoiding sequences even in some of the
simplest cases. (ii) A hierarchy of bounds using multiple lazy fingers,
addressing a recent question of Iacono and Langerman. (iii) The optimality of
the Move-to-root heuristic in the key-independent setting introduced by Iacono
(Algorithmica 2005). (iv) A new tool that allows combining any finite number of
sound structural properties. As an application, we show an upper bound on the
cost of a class of sequences that all known properties fail to capture. (v) The
equivalence between two families of BST properties. The observation on which
this connection is based was known before - we make it explicit, and apply it
to classical BST properties. (...)

Export

BibTeX

@online{Chalermsook2016PP,
TITLE = {The Landscape of Bounds for Binary Search Trees},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, L{\'a}szl{\'o} and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1603.04892},
EPRINT = {1603.04892},
EPRINTTYPE = {arXiv},
YEAR = {2016},
ABSTRACT = {Binary search trees (BSTs) with rotations can adapt to various kinds of structure in search sequences, achieving amortized access times substantially better than the Theta(log n) worst-case guarantee. Classical examples of structural properties include static optimality, sequential access, working set, key-independent optimality, and dynamic finger, all of which are now known to be achieved by the two famous online BST algorithms (Splay and Greedy). (...) In this paper, we introduce novel properties that explain the efficiency of sequences not captured by any of the previously known properties, and which provide new barriers to the dynamic optimality conjecture. We also establish connections between various properties, old and new. For instance, we show the following. (i) A tight bound of O(n log d) on the cost of Greedy for d-decomposable sequences. The result builds on the recent lazy finger result of Iacono and Langerman (SODA 2016). On the other hand, we show that lazy finger alone cannot explain the efficiency of pattern avoiding sequences even in some of the simplest cases. (ii) A hierarchy of bounds using multiple lazy fingers, addressing a recent question of Iacono and Langerman. (iii) The optimality of the Move-to-root heuristic in the key-independent setting introduced by Iacono (Algorithmica 2005). (iv) A new tool that allows combining any finite number of sound structural properties. As an application, we show an upper bound on the cost of a class of sequences that all known properties fail to capture. (v) The equivalence between two families of BST properties. The observation on which this connection is based was known before -- we make it explicit, and apply it to classical BST properties. (...)},
}

Endnote

%0 Report
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, László
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T The Landscape of Bounds for Binary Search Trees :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-FCC9-9
%U http://arxiv.org/abs/1603.04892
%D 2016
%X Binary search trees (BSTs) with rotations can adapt to various kinds of
structure in search sequences, achieving amortized access times substantially
better than the Theta(log n) worst-case guarantee. Classical examples of
structural properties include static optimality, sequential access, working
set, key-independent optimality, and dynamic finger, all of which are now known
to be achieved by the two famous online BST algorithms (Splay and Greedy).
(...)
In this paper, we introduce novel properties that explain the efficiency of
sequences not captured by any of the previously known properties, and which
provide new barriers to the dynamic optimality conjecture. We also establish
connections between various properties, old and new. For instance, we show the
following.
(i) A tight bound of O(n log d) on the cost of Greedy for d-decomposable
sequences. The result builds on the recent lazy finger result of Iacono and
Langerman (SODA 2016). On the other hand, we show that lazy finger alone cannot
explain the efficiency of pattern avoiding sequences even in some of the
simplest cases. (ii) A hierarchy of bounds using multiple lazy fingers,
addressing a recent question of Iacono and Langerman. (iii) The optimality of
the Move-to-root heuristic in the key-independent setting introduced by Iacono
(Algorithmica 2005). (iv) A new tool that allows combining any finite number of
sound structural properties. As an application, we show an upper bound on the
cost of a class of sequences that all known properties fail to capture. (v) The
equivalence between two families of BST properties. The observation on which
this connection is based was known before - we make it explicit, and apply it
to classical BST properties. (...)
%K Computer Science, Data Structures and Algorithms, cs.DS

[58]

C. Croitoru and K. Mehlhorn, “Opposition Frameworks,” in Logics in Artificial Intelligence (JELIA 2016), Larnaca, Cyprus, 2016.

Export

BibTeX

@inproceedings{DBLP:conf/jelia/CroitoruM16,
TITLE = {Opposition Frameworks},
AUTHOR = {Croitoru, Cosmina and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-319-48757-1},
DOI = {10.1007/978-3-319-48758-8_13},
PUBLISHER = {Springer},
YEAR = {2016},
DATE = {2016},
BOOKTITLE = {Logics in Artificial Intelligence (JELIA 2016)},
EDITOR = {Michael, Loizos and Kakas, Antonios},
PAGES = {190--206},
SERIES = {Lecture Notes in Artificial Intelligence},
VOLUME = {10021},
ADDRESS = {Larnaca, Cyprus},
}

Endnote

%0 Conference Proceedings
%A Croitoru, Cosmina
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Opposition Frameworks :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002C-57A8-4
%R 10.1007/978-3-319-48758-8_13
%D 2016
%B 15th European Conference on Logics in Artificial Intelligence
%Z date of event: 2016-11-09 - 2016-11-11
%C Larnaca, Cyprus
%B Logics in Artificial Intelligence
%E Michael, Loizos; Kakas, Antonios
%P 190 - 206
%I Springer
%@ 978-3-319-48757-1
%B Lecture Notes in Artificial Intelligence
%N 10021

[59]

O. Darwish and K. Mehlhorn, “Improved Balanced Flow Computation Using Parametric Flow,” Information Processing Letters, vol. 116, no. 9, 2016.

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BibTeX

@article{DarwishMehlhorn2016,
TITLE = {Improved Balanced Flow Computation Using Parametric Flow},
AUTHOR = {Darwish, Omar and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0020-0190},
DOI = {10.1016/j.ipl.2016.04.008},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2016},
DATE = {2016},
JOURNAL = {Information Processing Letters},
VOLUME = {116},
NUMBER = {9},
PAGES = {560--563},
}

Endnote

%0 Journal Article
%A Darwish, Omar
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improved Balanced Flow Computation Using Parametric Flow :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-FC7B-A
%R 10.1016/j.ipl.2016.04.008
%7 2016-04-22
%D 2016
%J Information Processing Letters
%V 116
%N 9
%& 560
%P 560 - 563
%I Elsevier
%C Amsterdam
%@ false

[60]

R. Duan, J. Garg, and K. Mehlhorn, “An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market,” in Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016), Arlington, VA, USA, 2016.

Abstract

We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. The improvement comes from a better understanding of the iterative price adjustment process, the improved balanced flow computation for nondegenerate instances, and a novel perturbation technique for achieving nondegeneracy.

Export

BibTeX

@inproceedings{DuanSODA2016,
TITLE = {An Improved Combinatorial Polynomial Algorithm for the Linear {Arrow}-{Debreu} Market},
AUTHOR = {Duan, Ran and Garg, Jugal and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-1-61197-433-1},
DOI = {10.1137/1.9781611974331.ch7},
PUBLISHER = {SIAM},
YEAR = {2016},
DATE = {2016},
ABSTRACT = {We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. The improvement comes from a better understanding of the iterative price adjustment process, the improved balanced flow computation for nondegenerate instances, and a novel perturbation technique for achieving nondegeneracy.},
BOOKTITLE = {Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2016)},
EDITOR = {Krauthgamer, Robert},
PAGES = {90--106},
ADDRESS = {Arlington, VA, USA},
}

Endnote

%0 Conference Proceedings
%A Duan, Ran
%A Garg, Jugal
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-81DD-9
%R 10.1137/1.9781611974331.ch7
%D 2016
%B Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2016-01-10 - 2016-01-12
%C Arlington, VA, USA
%X We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. The improvement comes from a better understanding of the iterative price adjustment process, the improved balanced flow computation for nondegenerate instances, and a novel perturbation technique for achieving nondegeneracy.
%B Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
%E Krauthgamer, Robert
%P 90 - 106
%I SIAM
%@ 978-1-61197-433-1

[61]

K. Elbassioni, K. Mehlhorn, and F. Ramezani, “Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design,” Theory of Computing Systems, vol. 59, no. 4, 2016.

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BibTeX

@article{ElbassioniTCS2016,
TITLE = {Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design},
AUTHOR = {Elbassioni, Khaled and Mehlhorn, Kurt and Ramezani, Fahimeh},
LANGUAGE = {eng},
ISSN = {1432-4350},
DOI = {10.1007/s00224-016-9704-2},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2016},
DATE = {2016},
JOURNAL = {Theory of Computing Systems},
VOLUME = {59},
NUMBER = {4},
PAGES = {641--663},
}

Endnote

%0 Journal Article
%A Elbassioni, Khaled
%A Mehlhorn, Kurt
%A Ramezani, Fahimeh
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002C-0B1C-9
%R 10.1007/s00224-016-9704-2
%7 2016
%D 2016
%J Theory of Computing Systems
%V 59
%N 4
%& 641
%P 641 - 663
%I Springer
%C New York, NY
%@ false

[62]

C.-C. Huang, T. Kavitha, K. Mehlhorn, and D. Michail, “Fair Matchings and Related Problems,” Algorithmica, vol. 74, no. 3, 2016.

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BibTeX

@article{Huang2016,
TITLE = {Fair Matchings and Related Problems},
AUTHOR = {Huang, Chien-Chung and Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-015-9994-9},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2016},
DATE = {2016},
JOURNAL = {Algorithmica},
VOLUME = {74},
NUMBER = {3},
PAGES = {1184--1203},
}

Endnote

%0 Journal Article
%A Huang, Chien-Chung
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Fair Matchings and Related Problems :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-115F-4
%R 10.1007/s00453-015-9994-9
%7 2016
%D 2016
%J Algorithmica
%V 74
%N 3
%& 1184
%P 1184 - 1203
%I Springer
%C New York, NY
%@ false

[63]

P. Kolev and K. Mehlhorn, “A Note On Spectral Clustering,” in 24th Annual European Symposium on Algorithms (ESA 2016), Aarhus, Denmark, 2016.

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BibTeX

@inproceedings{KolevESA2016,
TITLE = {A Note On Spectral Clustering},
AUTHOR = {Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1868-8969},
ISBN = {978-3-95977-015-6},
URL = {urn:nbn:de:0030-drops-63994},
DOI = {10.4230/LIPIcs.ESA.2016.57},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2016},
BOOKTITLE = {24th Annual European Symposium on Algorithms (ESA 2016)},
EDITOR = {Sankowski, Piotr and Zaroliagis, Christos},
PAGES = {1--14},
EID = {57},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {57},
ADDRESS = {Aarhus, Denmark},
}

Endnote

%0 Conference Proceedings
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Note On Spectral Clustering :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002B-4797-D
%U urn:nbn:de:0030-drops-63994
%R 10.4230/LIPIcs.ESA.2016.57
%D 2016
%B 24th Annual European Symposium on Algorithms
%Z date of event: 2016-08-22 - 2016-08-26
%C Aarhus, Denmark
%B 24th Annual European Symposium on Algorithms
%E Sankowski, Piotr; Zaroliagis, Christos
%P 1 - 14
%Z sequence number: 57
%I Schloss Dagstuhl
%@ 978-3-95977-015-6
%B Leibniz International Proceedings in Informatics
%N 57
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2016/6399/http://drops.dagstuhl.de/doku/urheberrecht1.html

[64]

K. Mehlhorn, “Algorithms and Programs: Erasmus Lecture 2014,” European Review, vol. 24, no. 1, 2016.

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BibTeX

@article{MehlhornErasmus2014,
TITLE = {Algorithms and Programs: Erasmus Lecture 2014},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1062-7987},
DOI = {10.1017/S1062798715000381},
PUBLISHER = {Cambridge University Press},
ADDRESS = {Cambridge},
YEAR = {2016},
DATE = {2016},
JOURNAL = {European Review},
VOLUME = {24},
NUMBER = {1},
PAGES = {4--16},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Algorithms and Programs: Erasmus Lecture 2014 :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-07A2-A
%R 10.1017/S1062798715000381
%7 2016
%D 2016
%J European Review
%V 24
%N 1
%& 4
%P 4 - 16
%I Cambridge University Press
%C Cambridge
%@ false

[65]

K. Mehlhorn and S. Saxena, “A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming,” Computer Science Review, vol. 22, 2016.

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BibTeX

@article{MehlhornSaxena2016,
TITLE = {A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming},
AUTHOR = {Mehlhorn, Kurt and Saxena, Sanjeev},
LANGUAGE = {eng},
DOI = {10.1016/j.cosrev.2016.07.001},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2016},
DATE = {2016},
JOURNAL = {Computer Science Review},
VOLUME = {22},
PAGES = {1--11},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Saxena, Sanjeev
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002D-7CA0-D
%R 10.1016/j.cosrev.2016.07.001
%7 2016
%D 2016
%J Computer Science Review
%V 22
%& 1
%P 1 - 11
%I Elsevier
%C Amsterdam

[66]

M. Sagraloff and K. Mehlhorn, “Computing Real Roots of Real Polynomials,” Journal of Symbolic Computation, vol. 73, 2016.

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BibTeX

@article{SagraloffJSC2016,
TITLE = {Computing Real Roots of Real Polynomials},
AUTHOR = {Sagraloff, Michael and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0747-7171},
DOI = {10.1016/j.jsc.2015.03.004},
PUBLISHER = {Academic Press},
ADDRESS = {London},
YEAR = {2016},
DATE = {2016},
JOURNAL = {Journal of Symbolic Computation},
VOLUME = {73},
PAGES = {46--86},
}

Endnote

%0 Journal Article
%A Sagraloff, Michael
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Computing Real Roots of Real Polynomials :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0025-0B82-A
%R 10.1016/j.jsc.2015.03.004
%7 2015
%D 2016
%J Journal of Symbolic Computation
%V 73
%& 46
%P 46 - 86
%I Academic Press
%C London
%@ false

2015

[67]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Pattern-avoiding Access in Binary Search Trees,” in FOCS 2015, IEEE 56th Annual Symposium on Foundations of Computer Science, Berkeley, CA, USA, 2015.

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BibTeX

@inproceedings{ChalermsookFOCS2015,
TITLE = {Pattern-avoiding Access in Binary Search Trees},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, L{\'a}szl{\'o} and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
DOI = {10.1109/FOCS.2015.32},
PUBLISHER = {IEEE},
YEAR = {2015},
DATE = {2015},
BOOKTITLE = {FOCS 2015, IEEE 56th Annual Symposium on Foundations of Computer Science},
PAGES = {410--423},
ADDRESS = {Berkeley, CA, USA},
}

Endnote

%0 Conference Proceedings
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, László
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Pattern-avoiding Access in Binary Search Trees :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-078B-F
%R 10.1109/FOCS.2015.32
%D 2015
%B IEEE 56th Annual Symposium on Foundations of Computer Science
%Z date of event: 2015-10-18 - 2015-10-20
%C Berkeley, CA, USA
%B FOCS 2015
%P 410 - 423
%I IEEE

[68]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Greedy Is an Almost Optimal Deque,” 2015. [Online]. Available: http://arxiv.org/abs/1506.08319. (arXiv: 1506.08319)

Abstract

In this paper we extend the geometric binary search tree (BST) model of
Demaine, Harmon, Iacono, Kane, and Patrascu (DHIKP) to accommodate for
insertions and deletions. Within this extended model, we study the online
Greedy BST algorithm introduced by DHIKP. Greedy BST is known to be equivalent
to a maximally greedy (but inherently offline) algorithm introduced
independently by Lucas in 1988 and Munro in 2000, conjectured to be dynamically
optimal.
With the application of forbidden-submatrix theory, we prove a quasilinear
upper bound on the performance of Greedy BST on deque sequences. It has been
conjectured (Tarjan, 1985) that splay trees (Sleator and Tarjan, 1983) can
serve such sequences in linear time. Currently neither splay trees, nor other
general-purpose BST algorithms are known to fulfill this requirement. As a
special case, we show that Greedy BST can serve output-restricted deque
sequences in linear time. A similar result is known for splay trees (Tarjan,
1985; Elmasry, 2004).
As a further application of the insert-delete model, we give a simple proof
that, given a set U of permutations of [n], the access cost of any BST
algorithm is Omega(log |U| + n) on "most" of the permutations from U. In
particular, this implies that the access cost for a random permutation of [n]
is Omega(n log n) with high probability.
Besides the splay tree noted before, Greedy BST has recently emerged as a
plausible candidate for dynamic optimality. Compared to splay trees, much less
effort has gone into analyzing Greedy BST. Our work is intended as a step
towards a full understanding of Greedy BST, and we remark that
forbidden-submatrix arguments seem particularly well suited for carrying out
this program.

Export

BibTeX

@online{Chalermsookabs/1506.08319,
TITLE = {Greedy Is an Almost Optimal Deque},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, Laszlo and Mehlhorn, Kurt and Saranurak, Thatchaphol},
URL = {http://arxiv.org/abs/1506.08319},
EPRINT = {1506.08319},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {In this paper we extend the geometric binary search tree (BST) model of Demaine, Harmon, Iacono, Kane, and Patrascu (DHIKP) to accommodate for insertions and deletions. Within this extended model, we study the online Greedy BST algorithm introduced by DHIKP. Greedy BST is known to be equivalent to a maximally greedy (but inherently offline) algorithm introduced independently by Lucas in 1988 and Munro in 2000, conjectured to be dynamically optimal. With the application of forbidden-submatrix theory, we prove a quasilinear upper bound on the performance of Greedy BST on deque sequences. It has been conjectured (Tarjan, 1985) that splay trees (Sleator and Tarjan, 1983) can serve such sequences in linear time. Currently neither splay trees, nor other general-purpose BST algorithms are known to fulfill this requirement. As a special case, we show that Greedy BST can serve output-restricted deque sequences in linear time. A similar result is known for splay trees (Tarjan, 1985; Elmasry, 2004). As a further application of the insert-delete model, we give a simple proof that, given a set U of permutations of [n], the access cost of any BST algorithm is Omega(log |U| + n) on "most" of the permutations from U. In particular, this implies that the access cost for a random permutation of [n] is Omega(n log n) with high probability. Besides the splay tree noted before, Greedy BST has recently emerged as a plausible candidate for dynamic optimality. Compared to splay trees, much less effort has gone into analyzing Greedy BST. Our work is intended as a step towards a full understanding of Greedy BST, and we remark that forbidden-submatrix arguments seem particularly well suited for carrying out this program.},
}

Endnote

%0 Report
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, Laszlo
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Greedy Is an Almost Optimal Deque :
%U http://hdl.handle.net/11858/00-001M-0000-0027-D400-5
%U http://arxiv.org/abs/1506.08319
%D 2015
%X In this paper we extend the geometric binary search tree (BST) model of
Demaine, Harmon, Iacono, Kane, and Patrascu (DHIKP) to accommodate for
insertions and deletions. Within this extended model, we study the online
Greedy BST algorithm introduced by DHIKP. Greedy BST is known to be equivalent
to a maximally greedy (but inherently offline) algorithm introduced
independently by Lucas in 1988 and Munro in 2000, conjectured to be dynamically
optimal.
With the application of forbidden-submatrix theory, we prove a quasilinear
upper bound on the performance of Greedy BST on deque sequences. It has been
conjectured (Tarjan, 1985) that splay trees (Sleator and Tarjan, 1983) can
serve such sequences in linear time. Currently neither splay trees, nor other
general-purpose BST algorithms are known to fulfill this requirement. As a
special case, we show that Greedy BST can serve output-restricted deque
sequences in linear time. A similar result is known for splay trees (Tarjan,
1985; Elmasry, 2004).
As a further application of the insert-delete model, we give a simple proof
that, given a set U of permutations of [n], the access cost of any BST
algorithm is Omega(log |U| + n) on "most" of the permutations from U. In
particular, this implies that the access cost for a random permutation of [n]
is Omega(n log n) with high probability.
Besides the splay tree noted before, Greedy BST has recently emerged as a
plausible candidate for dynamic optimality. Compared to splay trees, much less
effort has gone into analyzing Greedy BST. Our work is intended as a step
towards a full understanding of Greedy BST, and we remark that
forbidden-submatrix arguments seem particularly well suited for carrying out
this program.
%K Computer Science, Data Structures and Algorithms, cs.DS

[69]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Greedy Is an Almost Optimal Deque,” in Algorithms and Data Structures (WADS 2015), Victoria, Canada, 2015.

Export

BibTeX

@inproceedings{ChalermsookWADS2015,
TITLE = {Greedy Is an Almost Optimal Deque},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, L{\'a}sl{\'o} and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
ISBN = {978-3-319-21839-7},
DOI = {10.1007/978-3-319-21840-3_13},
PUBLISHER = {Springer},
YEAR = {2015},
DATE = {2015},
BOOKTITLE = {Algorithms and Data Structures (WADS 2015)},
EDITOR = {Dehne, Frank and Sack, J{\"o}rg-R{\"u}diger and Stege, Ulrike},
PAGES = {152--165},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {9214},
ADDRESS = {Victoria, Canada},
}

Endnote

%0 Conference Proceedings
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, Lásló
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Greedy Is an Almost Optimal Deque :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-8F41-6
%R 10.1007/978-3-319-21840-3_13
%D 2015
%B 14th International Symposium on Algorithms and Data Structure
%Z date of event: 2015-08-05 - 2015-08-07
%C Victoria, Canada
%B Algorithms and Data Structures
%E Dehne, Frank; Sack, Jörg-Rüdiger; Stege, Ulrike
%P 152 - 165
%I Springer
%@ 978-3-319-21839-7
%B Lecture Notes in Computer Science
%N 9214

[70]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Self-Adjusting Binary Search Trees: What Makes Them Tick?,” in Algorithms -- ESA 2015, Patras, Greece, 2015.

Export

BibTeX

@inproceedings{ChalermsookESA2015,
TITLE = {Self-Adjusting Binary Search Trees: {W}hat Makes Them Tick?},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, Laszlo and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
ISBN = {978-3-662-4834},
DOI = {10.1007/978-3-662-48350-3_26},
PUBLISHER = {Springer},
YEAR = {2015},
DATE = {2015},
BOOKTITLE = {Algorithms -- ESA 2015},
EDITOR = {Bansal, Nikhil and Finocchi, Irene},
PAGES = {300--312},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {9294},
ADDRESS = {Patras, Greece},
}

Endnote

%0 Conference Proceedings
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, Laszlo
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Self-Adjusting Binary Search Trees: What Makes Them Tick? :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-667A-C
%R 10.1007/978-3-662-48350-3_26
%D 2015
%B 23rd Annual European Symposium on Algorithms
%Z date of event: 2015-09-14 - 2015-09-16
%C Patras, Greece
%B Algorithms -- ESA 2015
%E Bansal, Nikhil; Finocchi, Irene
%P 300 - 312
%I Springer
%@ 978-3-662-4834
%B Lecture Notes in Computer Science
%N 9294

[71]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Pattern-avoiding Access in Binary Search Trees,” 2015. [Online]. Available: http://arxiv.org/abs/1507.06953. (arXiv: 1507.06953)

Abstract

The dynamic optimality conjecture is perhaps the most fundamental open
question about binary search trees (BST). It postulates the existence of an
asymptotically optimal online BST, i.e. one that is constant factor competitive
with any BST on any input access sequence. The two main candidates for dynamic
optimality in the literature are splay trees [Sleator and Tarjan, 1985], and
Greedy [Lucas, 1988; Munro, 2000; Demaine et al. 2009] [..]
Dynamic optimality is trivial for almost all sequences: the optimum access
cost of most length-n sequences is Theta(n log n), achievable by any balanced
BST. Thus, the obvious missing step towards the conjecture is an understanding
of the "easy" access sequences. [..] The difficulty of proving dynamic
optimality is witnessed by highly restricted special cases that remain
unresolved; one prominent example is the traversal conjecture [Sleator and
Tarjan, 1985], which states that preorder sequences (whose optimum is linear)
are linear-time accessed by splay trees; no online BST is known to satisfy this
conjecture.
In this paper, we prove two different relaxations of the traversal conjecture
for Greedy: (i) Greedy is almost linear for preorder traversal, (ii) if a
linear-time preprocessing is allowed, Greedy is in fact linear. These
statements are corollaries of our more general results that express the
complexity of access sequences in terms of a pattern avoidance parameter k.
[..] To our knowledge, these are the first upper bounds for Greedy that are not
known to hold for any other online BST. To obtain these results we identify an
input-revealing property of Greedy. Informally, this means that the execution
log partially reveals the structure of the access sequence. This property
facilitates the use of rich technical tools from forbidden submatrix theory.
[Abridged]

Export

BibTeX

@online{ChalermsookArXiv2015,
TITLE = {Pattern-avoiding Access in Binary Search Trees},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, L{\'a}szl{\'o} and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1507.06953},
EPRINT = {1507.06953},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {The dynamic optimality conjecture is perhaps the most fundamental open question about binary search trees (BST). It postulates the existence of an asymptotically optimal online BST, i.e. one that is constant factor competitive with any BST on any input access sequence. The two main candidates for dynamic optimality in the literature are splay trees [Sleator and Tarjan, 1985], and Greedy [Lucas, 1988; Munro, 2000; Demaine et al. 2009] [..] Dynamic optimality is trivial for almost all sequences: the optimum access cost of most length-n sequences is Theta(n log n), achievable by any balanced BST. Thus, the obvious missing step towards the conjecture is an understanding of the "easy" access sequences. [..] The difficulty of proving dynamic optimality is witnessed by highly restricted special cases that remain unresolved; one prominent example is the traversal conjecture [Sleator and Tarjan, 1985], which states that preorder sequences (whose optimum is linear) are linear-time accessed by splay trees; no online BST is known to satisfy this conjecture. In this paper, we prove two different relaxations of the traversal conjecture for Greedy: (i) Greedy is almost linear for preorder traversal, (ii) if a linear-time preprocessing is allowed, Greedy is in fact linear. These statements are corollaries of our more general results that express the complexity of access sequences in terms of a pattern avoidance parameter k. [..] To our knowledge, these are the first upper bounds for Greedy that are not known to hold for any other online BST. To obtain these results we identify an input-revealing property of Greedy. Informally, this means that the execution log partially reveals the structure of the access sequence. This property facilitates the use of rich technical tools from forbidden submatrix theory. [Abridged]},
}

Endnote

%0 Report
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, László
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Pattern-avoiding Access in Binary Search Trees :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-8F4C-0
%U http://arxiv.org/abs/1507.06953
%D 2015
%X The dynamic optimality conjecture is perhaps the most fundamental open
question about binary search trees (BST). It postulates the existence of an
asymptotically optimal online BST, i.e. one that is constant factor competitive
with any BST on any input access sequence. The two main candidates for dynamic
optimality in the literature are splay trees [Sleator and Tarjan, 1985], and
Greedy [Lucas, 1988; Munro, 2000; Demaine et al. 2009] [..]
Dynamic optimality is trivial for almost all sequences: the optimum access
cost of most length-n sequences is Theta(n log n), achievable by any balanced
BST. Thus, the obvious missing step towards the conjecture is an understanding
of the "easy" access sequences. [..] The difficulty of proving dynamic
optimality is witnessed by highly restricted special cases that remain
unresolved; one prominent example is the traversal conjecture [Sleator and
Tarjan, 1985], which states that preorder sequences (whose optimum is linear)
are linear-time accessed by splay trees; no online BST is known to satisfy this
conjecture.
In this paper, we prove two different relaxations of the traversal conjecture
for Greedy: (i) Greedy is almost linear for preorder traversal, (ii) if a
linear-time preprocessing is allowed, Greedy is in fact linear. These
statements are corollaries of our more general results that express the
complexity of access sequences in terms of a pattern avoidance parameter k.
[..] To our knowledge, these are the first upper bounds for Greedy that are not
known to hold for any other online BST. To obtain these results we identify an
input-revealing property of Greedy. Informally, this means that the execution
log partially reveals the structure of the access sequence. This property
facilitates the use of rich technical tools from forbidden submatrix theory.
[Abridged]
%K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Combinatorics, math.CO

[72]

P. Chalermsook, M. Goswami, L. Kozma, K. Mehlhorn, and T. Saranurak, “Self-Adjusting Binary Search Trees: What Makes Them Tick?,” 2015. [Online]. Available: http://arxiv.org/abs/1503.03105. (arXiv: 1503.03105)

Abstract

Splay trees (Sleator and Tarjan) satisfy the so-called access lemma. Many of
the nice properties of splay trees follow from it. What makes self-adjusting
binary search trees (BSTs) satisfy the access lemma? After each access,
self-adjusting BSTs replace the search path by a tree on the same set of nodes
(the after-tree). We identify two simple combinatorial properties of the search
path and the after-tree that imply the access lemma. Our main result (i)
implies the access lemma for all minimally self-adjusting BST algorithms for
which it was known to hold: splay trees and their generalization to the class
of local algorithms (Subramanian, Georgakopoulos and Mc-Clurkin), as well as
Greedy BST, introduced by Demaine et al. and shown to satisfy the access lemma
by Fox, (ii) implies that BST algorithms based on "strict" depth-halving
satisfy the access lemma, addressing an open question that was raised several
times since 1985, and (iii) yields an extremely short proof for the O(log n log
log n) amortized access cost for the path-balance heuristic (proposed by
Sleator), matching the best known bound (Balasubramanian and Raman) to a
lower-order factor.
One of our combinatorial properties is locality. We show that any
BST-algorithm that satisfies the access lemma via the sum-of-log (SOL)
potential is necessarily local. The other property states that the sum of the
number of leaves of the after-tree plus the number of side alternations in the
search path must be at least a constant fraction of the length of the search
path. We show that a weak form of this property is necessary for sequential
access to be linear.

Export

BibTeX

@online{Chalermsook/abs/1503.03105,
TITLE = {Self-Adjusting Binary Search Trees: What Makes Them Tick?},
AUTHOR = {Chalermsook, Parinya and Goswami, Mayank and Kozma, Laszlo and Mehlhorn, Kurt and Saranurak, Thatchaphol},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1503.03105},
EPRINT = {1503.03105},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {Splay trees (Sleator and Tarjan) satisfy the so-called access lemma. Many of the nice properties of splay trees follow from it. What makes self-adjusting binary search trees (BSTs) satisfy the access lemma? After each access, self-adjusting BSTs replace the search path by a tree on the same set of nodes (the after-tree). We identify two simple combinatorial properties of the search path and the after-tree that imply the access lemma. Our main result (i) implies the access lemma for all minimally self-adjusting BST algorithms for which it was known to hold: splay trees and their generalization to the class of local algorithms (Subramanian, Georgakopoulos and Mc-Clurkin), as well as Greedy BST, introduced by Demaine et al. and shown to satisfy the access lemma by Fox, (ii) implies that BST algorithms based on "strict" depth-halving satisfy the access lemma, addressing an open question that was raised several times since 1985, and (iii) yields an extremely short proof for the O(log n log log n) amortized access cost for the path-balance heuristic (proposed by Sleator), matching the best known bound (Balasubramanian and Raman) to a lower-order factor. One of our combinatorial properties is locality. We show that any BST-algorithm that satisfies the access lemma via the sum-of-log (SOL) potential is necessarily local. The other property states that the sum of the number of leaves of the after-tree plus the number of side alternations in the search path must be at least a constant fraction of the length of the search path. We show that a weak form of this property is necessary for sequential access to be linear.},
}

Endnote

%0 Report
%A Chalermsook, Parinya
%A Goswami, Mayank
%A Kozma, Laszlo
%A Mehlhorn, Kurt
%A Saranurak, Thatchaphol
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Self-Adjusting Binary Search Trees: What Makes Them Tick? :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0027-D3FB-E
%U http://arxiv.org/abs/1503.03105
%D 2015
%X Splay trees (Sleator and Tarjan) satisfy the so-called access lemma. Many of
the nice properties of splay trees follow from it. What makes self-adjusting
binary search trees (BSTs) satisfy the access lemma? After each access,
self-adjusting BSTs replace the search path by a tree on the same set of nodes
(the after-tree). We identify two simple combinatorial properties of the search
path and the after-tree that imply the access lemma. Our main result (i)
implies the access lemma for all minimally self-adjusting BST algorithms for
which it was known to hold: splay trees and their generalization to the class
of local algorithms (Subramanian, Georgakopoulos and Mc-Clurkin), as well as
Greedy BST, introduced by Demaine et al. and shown to satisfy the access lemma
by Fox, (ii) implies that BST algorithms based on "strict" depth-halving
satisfy the access lemma, addressing an open question that was raised several
times since 1985, and (iii) yields an extremely short proof for the O(log n log
log n) amortized access cost for the path-balance heuristic (proposed by
Sleator), matching the best known bound (Balasubramanian and Raman) to a
lower-order factor.
One of our combinatorial properties is locality. We show that any
BST-algorithm that satisfies the access lemma via the sum-of-log (SOL)
potential is necessarily local. The other property states that the sum of the
number of leaves of the after-tree plus the number of side alternations in the
search path must be at least a constant fraction of the length of the search
path. We show that a weak form of this property is necessary for sequential
access to be linear.
%K Computer Science, Data Structures and Algorithms, cs.DS

[73]

O. Darwish and K. Mehlhorn, “Improved Balanced Flow Computation Using Parametric Flow,” 2015. [Online]. Available: http://arxiv.org/abs/1512.05974. (arXiv: 1512.05974)

Abstract

We present a new algorithm for computing balanced flows in equality networks
arising in market equilibrium computations. The current best time bound for
computing balanced flows in such networks requires $O(n)$ maxflow computations,
where $n$ is the number of nodes in the network [Devanur et al. 2008]. Our
algorithm requires only a single parametric flow computation. The best
algorithm for computing parametric flows [Gallo et al. 1989] is only by a
logarithmic factor slower than the best algorithms for computing maxflows.
Hence, the running time of the algorithms in [Devanur et al. 2008] and [Duan
and Mehlhorn 2015] for computing market equilibria in linear Fisher and
Arrow-Debreu markets improve by almost a factor of $n$.

Export

BibTeX

@online{DarwishMehlhorn2015,
TITLE = {Improved Balanced Flow Computation Using Parametric Flow},
AUTHOR = {Darwish, Omar and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1512.05974},
EPRINT = {1512.05974},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {We present a new algorithm for computing balanced flows in equality networks arising in market equilibrium computations. The current best time bound for computing balanced flows in such networks requires $O(n)$ maxflow computations, where $n$ is the number of nodes in the network [Devanur et al. 2008]. Our algorithm requires only a single parametric flow computation. The best algorithm for computing parametric flows [Gallo et al. 1989] is only by a logarithmic factor slower than the best algorithms for computing maxflows. Hence, the running time of the algorithms in [Devanur et al. 2008] and [Duan and Mehlhorn 2015] for computing market equilibria in linear Fisher and Arrow-Debreu markets improve by almost a factor of $n$.},
}

Endnote

%0 Report
%A Darwish, Omar
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improved Balanced Flow Computation Using Parametric Flow :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0029-4A62-F
%U http://arxiv.org/abs/1512.05974
%D 2015
%X We present a new algorithm for computing balanced flows in equality networks
arising in market equilibrium computations. The current best time bound for
computing balanced flows in such networks requires $O(n)$ maxflow computations,
where $n$ is the number of nodes in the network [Devanur et al. 2008]. Our
algorithm requires only a single parametric flow computation. The best
algorithm for computing parametric flows [Gallo et al. 1989] is only by a
logarithmic factor slower than the best algorithms for computing maxflows.
Hence, the running time of the algorithms in [Devanur et al. 2008] and [Duan
and Mehlhorn 2015] for computing market equilibria in linear Fisher and
Arrow-Debreu markets improve by almost a factor of $n$.
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computer Science and Game Theory, cs.GT

[74]

R. Duan and K. Mehlhorn, “A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market,” Information and Computation, vol. 243, 2015.

Export

BibTeX

@article{Duan2015,
TITLE = {A Combinatorial Polynomial Algorithm for the Linear {Arrow}-{Debreu} Market},
AUTHOR = {Duan, Ran and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0890-5401},
DOI = {10.1016/j.ic.2014.12.009},
PUBLISHER = {Academic Press},
ADDRESS = {San Diego},
YEAR = {2015},
DATE = {2015},
JOURNAL = {Information and Computation},
VOLUME = {243},
PAGES = {112--132},
}

Endnote

%0 Journal Article
%A Duan, Ran
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0027-AC93-6
%R 10.1016/j.ic.2014.12.009
%7 2015
%D 2015
%J Information and Computation
%V 243
%& 112
%P 112 - 132
%I Academic Press
%C San Diego
%@ false

[75]

R. Duan, J. Garg, and K. Mehlhorn, “An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market,” 2015. [Online]. Available: http://arxiv.org/abs/1510.02694. (arXiv: 1510.02694)

Abstract

We present an improved combinatorial algorithm for the computation of
equilibrium prices in the linear Arrow-Debreu model. For a market with $n$
agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7
\log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a
factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan
and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. The improvement
comes from a better understanding of the iterative price adjustment process,
the improved balanced flow computation for nondegenerate instances, and a novel
perturbation technique for achieving nondegeneracy.

Export

BibTeX

@online{Ranarxiv15,
TITLE = {An Improved Combinatorial Polynomial Algorithm for the {A}rrow-{D}ebreu Markets},
AUTHOR = {Duan, Ran and Garg, Jugal and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1510.02694},
EPRINT = {1510.02694},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. The improvement comes from a better understanding of the iterative price adjustment process, the improved balanced flow computation for nondegenerate instances, and a novel perturbation technique for achieving nondegeneracy.},
}

Endnote

%0 Report
%A Duan, Ran
%A Garg, Jugal
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T An Improved Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002C-88EC-3
%U http://arxiv.org/abs/1510.02694
%D 2015
%8 16.10.2015
%X We present an improved combinatorial algorithm for the computation of
equilibrium prices in the linear Arrow-Debreu model. For a market with $n$
agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7
\log^3 (nU))$ time. This improves upon the previously best algorithm of Ye by a
factor of $\tOmega(n)$. The algorithm refines the algorithm described by Duan
and Mehlhorn and improves it by a factor of $\tOmega(n^3)$. The improvement
comes from a better understanding of the iterative price adjustment process,
the improved balanced flow computation for nondegenerate instances, and a novel
perturbation technique for achieving nondegeneracy.
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computer Science and Game Theory, cs.GT

[76]

K. Elbassioni, K. Mehlhorn, and F. Ramezani, “Towards More Practical Linear Programming-Based Techniques for Algorithmic Mechanism Design,” in Algorithmic Game Theory (SAGT 2015), Saarbrücken, Germany, 2015.

Export

BibTeX

@inproceedings{ElbassioniSAGT2015,
TITLE = {Towards More Practical Linear Programming-Based Techniques for Algorithmic Mechanism Design},
AUTHOR = {Elbassioni, Khaled and Mehlhorn, Kurt and Ramezani, Fahimeh},
LANGUAGE = {eng},
ISBN = {978-3-662-48432-6},
DOI = {10.1007/978-3-662-48433-3_8},
PUBLISHER = {Springer},
YEAR = {2015},
DATE = {2015},
BOOKTITLE = {Algorithmic Game Theory (SAGT 2015)},
EDITOR = {Hoefer, Martin},
PAGES = {98--109},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {9347},
ADDRESS = {Saarbr{\"u}cken, Germany},
}

Endnote

%0 Conference Proceedings
%A Elbassioni, Khaled
%A Mehlhorn, Kurt
%A Ramezani, Fahimeh
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Towards More Practical Linear Programming-Based Techniques for Algorithmic Mechanism Design :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-8F3C-3
%R 10.1007/978-3-662-48433-3_8
%D 2015
%B 8th International Symposium on Algorithmic Game Theory
%Z date of event: 2015-09-28 - 2015-09-30
%C Saarbrücken, Germany
%B Algorithmic Game Theory
%E Hoefer, Martin
%P 98 - 109
%I Springer
%@ 978-3-662-48432-6
%B Lecture Notes in Computer Science
%N 9347

[77]

K. Elbassioni, K. Makino, K. Mehlhorn, and F. Ramezani, “On Randomized Fictitious Play for Approximating Saddle Points Over Convex Sets,” Algorithmica, vol. 73, no. 2, 2015.

Export

BibTeX

@article{Elbassioni_Algorithmica73,
TITLE = {On Randomized Fictitious Play for Approximating Saddle Points Over Convex Sets},
AUTHOR = {Elbassioni, Khaled and Makino, Kazuhisa and Mehlhorn, Kurt and Ramezani, Fahimeh},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-014-9902-8},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2015},
DATE = {2015},
JOURNAL = {Algorithmica},
VOLUME = {73},
NUMBER = {2},
PAGES = {441--459},
}

Endnote

%0 Journal Article
%A Elbassioni, Khaled
%A Makino, Kazuhisa
%A Mehlhorn, Kurt
%A Ramezani, Fahimeh
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Randomized Fictitious Play for Approximating Saddle Points Over
Convex Sets :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-669E-B
%R 10.1007/s00453-014-9902-8
%7 2015
%D 2015
%J Algorithmica
%V 73
%N 2
%& 441
%P 441 - 459
%I Springer
%C New York, NY
%@ false

[78]

P. Kolev and K. Mehlhorn, “A Note On Spectral Clustering,” 2015. [Online]. Available: http://arxiv.org/abs/1509.09188. (arXiv: 1509.09188)

Abstract

Let $G=(V,E)$ be an undirected graph, $\lambda_k$ the $k$th smallest
eigenvalue of the normalized Laplacian matrix of $G$, and $\rho(k)$ the
smallest value of the maximal conductance over all $k$-way partitions
$S_1,\dots,S_k$ of $V$.
Peng et al. [PSZ15] gave the first rigorous analysis of $k$-clustering
algorithms that use spectral embedding and $k$-means clustering algorithms to
partition the vertices of a graph $G$ into $k$ disjoint subsets. Their analysis
builds upon a gap parameter $\Upsilon=\rho(k)/\lambda_{k+1}$ that was
introduced by Oveis Gharan and Trevisan [GT14]. In their analysis Peng et al.
[PSZ15] assume a gap assumption $\Upsilon\geq\Omega(\mathrm{APR}\cdot k^3)$,
where $\mathrm{APR}>1$ is the approximation ratio of a $k$-means clustering
algorithm.
We exhibit an error in one of their Lemmas and provide a correction. With the
correction the proof by Peng et al. [PSZ15] requires a stronger gap assumption
$\Upsilon\geq\Omega(\mathrm{APR}\cdot k^4)$.
Our main contribution is to improve the analysis in [PSZ15] by an $O(k)$
factor. We demonstrate that a gap assumption $\Psi\geq \Omega(\mathrm{APR}\cdot
k^3)$ suffices, where $\Psi=\rho_{avr}(k)/\lambda_{k+1}$ and $\rho_{avr}(k)$ is
the value of the average conductance of a partition $S_1,\dots,S_k$ of $V$ that
yields $\rho(k)$.

Export

BibTeX

@online{KolevArXiv2015,
TITLE = {A Note On Spectral Clustering},
AUTHOR = {Kolev, Pavel and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1509.09188},
EPRINT = {1509.09188},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {Let $G=(V,E)$ be an undirected graph, $\lambda_k$ the $k$th smallest eigenvalue of the normalized Laplacian matrix of $G$, and $\rho(k)$ the smallest value of the maximal conductance over all $k$-way partitions $S_1,\dots,S_k$ of $V$. Peng et al. [PSZ15] gave the first rigorous analysis of $k$-clustering algorithms that use spectral embedding and $k$-means clustering algorithms to partition the vertices of a graph $G$ into $k$ disjoint subsets. Their analysis builds upon a gap parameter $\Upsilon=\rho(k)/\lambda_{k+1}$ that was introduced by Oveis Gharan and Trevisan [GT14]. In their analysis Peng et al. [PSZ15] assume a gap assumption $\Upsilon\geq\Omega(\mathrm{APR}\cdot k^3)$, where $\mathrm{APR}>1$ is the approximation ratio of a $k$-means clustering algorithm. We exhibit an error in one of their Lemmas and provide a correction. With the correction the proof by Peng et al. [PSZ15] requires a stronger gap assumption $\Upsilon\geq\Omega(\mathrm{APR}\cdot k^4)$. Our main contribution is to improve the analysis in [PSZ15] by an $O(k)$ factor. We demonstrate that a gap assumption $\Psi\geq \Omega(\mathrm{APR}\cdot k^3)$ suffices, where $\Psi=\rho_{avr}(k)/\lambda_{k+1}$ and $\rho_{avr}(k)$ is the value of the average conductance of a partition $S_1,\dots,S_k$ of $V$ that yields $\rho(k)$.},
}

Endnote

%0 Report
%A Kolev, Pavel
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Note On Spectral Clustering :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-8F4F-A
%U http://arxiv.org/abs/1509.09188
%D 2015
%X Let $G=(V,E)$ be an undirected graph, $\lambda_k$ the $k$th smallest
eigenvalue of the normalized Laplacian matrix of $G$, and $\rho(k)$ the
smallest value of the maximal conductance over all $k$-way partitions
$S_1,\dots,S_k$ of $V$.
Peng et al. [PSZ15] gave the first rigorous analysis of $k$-clustering
algorithms that use spectral embedding and $k$-means clustering algorithms to
partition the vertices of a graph $G$ into $k$ disjoint subsets. Their analysis
builds upon a gap parameter $\Upsilon=\rho(k)/\lambda_{k+1}$ that was
introduced by Oveis Gharan and Trevisan [GT14]. In their analysis Peng et al.
[PSZ15] assume a gap assumption $\Upsilon\geq\Omega(\mathrm{APR}\cdot k^3)$,
where $\mathrm{APR}>1$ is the approximation ratio of a $k$-means clustering
algorithm.
We exhibit an error in one of their Lemmas and provide a correction. With the
correction the proof by Peng et al. [PSZ15] requires a stronger gap assumption
$\Upsilon\geq\Omega(\mathrm{APR}\cdot k^4)$.
Our main contribution is to improve the analysis in [PSZ15] by an $O(k)$
factor. We demonstrate that a gap assumption $\Psi\geq \Omega(\mathrm{APR}\cdot
k^3)$ suffices, where $\Psi=\rho_{avr}(k)/\lambda_{k+1}$ and $\rho_{avr}(k)$ is
the value of the average conductance of a partition $S_1,\dots,S_k$ of $V$ that
yields $\rho(k)$.
%K Computer Science, Discrete Mathematics, cs.DM

[79]

K. Mehlhorn and S. Saxena, “A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming,” 2015. [Online]. Available: http://arxiv.org/abs/1510.03339. (arXiv: 1510.03339)

Abstract

Linear programming is now included in algorithm undergraduate and
postgraduate courses for computer science majors. We show that it is possible
to teach interior-point methods directly to students with just minimal
knowledge of linear algebra.

Export

BibTeX

@online{MehlhornSaxena2015,
TITLE = {A Still Simpler Way of Introducing the Interior-Point Method for Linear Programming},
AUTHOR = {Mehlhorn, Kurt and Saxena, Sanjeev},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1510.03339},
EPRINT = {1510.03339},
EPRINTTYPE = {arXiv},
YEAR = {2015},
ABSTRACT = {Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We show that it is possible to teach interior-point methods directly to students with just minimal knowledge of linear algebra.},
}

Endnote

%0 Report
%A Mehlhorn, Kurt
%A Saxena, Sanjeev
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T A Still Simpler Way of Introducing the Interior-Point Method for Linear
Programming :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-F70B-6
%U http://arxiv.org/abs/1510.03339
%D 2015
%X Linear programming is now included in algorithm undergraduate and
postgraduate courses for computer science majors. We show that it is possible
to teach interior-point methods directly to students with just minimal
knowledge of linear algebra.
%K Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Optimization and Control, math.OC

[80]

K. Mehlhorn, M. Sagraloff, and P. Wang, “From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition,” Journal of Symbolic Computation, vol. 66, 2015.

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BibTeX

@article{MehlhornSagraloffWang2015,
TITLE = {From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition},
AUTHOR = {Mehlhorn, Kurt and Sagraloff, Michael and Wang, Pengming},
LANGUAGE = {eng},
ISSN = {0747-7171},
DOI = {10.1016/j.jsc.2014.02.001},
PUBLISHER = {Academic Press},
ADDRESS = {London},
YEAR = {2015},
DATE = {2015},
JOURNAL = {Journal of Symbolic Computation},
VOLUME = {66},
PAGES = {34--69},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Sagraloff, Michael
%A Wang, Pengming
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T From Approximate Factorization to Root Isolation with Application to
Cylindrical Algebraic Decomposition :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-36CF-A
%R 10.1016/j.jsc.2014.02.001
%7 2014-02-21
%D 2015
%J Journal of Symbolic Computation
%V 66
%& 34
%P 34 - 69
%I Academic Press
%C London
%@ false

[81]

K. Mehlhorn, “On the Implementation of Combinatorial Algorithms for the Linear Exchange Market,” in Algorithms, Probability, Networks, and Games, Berlin: Springer, 2015.

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BibTeX

@incollection{MehlhornLNCS9295,
TITLE = {On the Implementation of Combinatorial Algorithms for the Linear Exchange Market},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-319-24023-7},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2015},
DATE = {2015},
BOOKTITLE = {Algorithms, Probability, Networks, and Games},
EDITOR = {Zaroliagis, Christos and Pantziou, Grammati and Kontogianni, Spyros},
PAGES = {87--94},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {9295},
}

Endnote

%0 Book Section
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On the Implementation of Combinatorial Algorithms for the Linear Exchange Market :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0028-8F36-F
%D 2015
%B Algorithms, Probability, Networks, and Games
%E Zaroliagis, Christos; Pantziou, Grammati; Kontogianni, Spyros; Spirakis, Paul G.
%P 87 - 94
%I Springer
%C Berlin
%@ 978-3-319-24023-7
%S Lecture Notes in Computer Science
%N 9295

[82]

K. Mehlhorn, “From Theory to Library of Efficient Data Types and Algorithms (LEDA) and Algorithm Engineering,” in The Human Face of Computing, London: Imperial College Press, 2015.

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BibTeX

@incollection{MehlhornLEDA2015,
TITLE = {From Theory to Library of Efficient Data Types and Algorithms ({LEDA}) and Algorithm Engineering},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-1-78326-643-2; 978-1-78326-645-6},
DOI = {10.1142/9781783266449_0005},
PUBLISHER = {Imperial College Press},
ADDRESS = {London},
YEAR = {2015},
DATE = {2015},
BOOKTITLE = {The Human Face of Computing},
EDITOR = {Calude, Christian S.},
PAGES = {59--71},
SERIES = {Advances in Computer Science and Engineering},
VOLUME = {9},
}

Endnote

%0 Book Section
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T From Theory to Library of Efficient Data Types and Algorithms (LEDA) and Algorithm Engineering : Chapter 5
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002A-0799-F
%R 10.1142/9781783266449_0005
%D 2015
%B The Human Face of Computing
%E Calude, Christian S.
%P 59 - 71
%I Imperial College Press
%C London
%@ 978-1-78326-643-2 978-1-78326-645-6
%S Advances in Computer Science and Engineering
%N 9

2014

[83]

E. Alkassar, S. Böhme, K. Mehlhorn, and C. Rizkallah, “A Framework for the Verification of Certifying Computations,” Journal of Automated Reasoning, vol. 52, no. 3, 2014.

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BibTeX

@article{AlkassarJAR2014,
TITLE = {A Framework for the Verification of Certifying Computations},
AUTHOR = {Alkassar, Eyad and B{\"o}hme, Sascha and Mehlhorn, Kurt and Rizkallah, Christine},
LANGUAGE = {eng},
ISSN = {0168-7433; 1573-0670},
DOI = {10.1007/s10817-013-9289-2},
PUBLISHER = {Springer},
ADDRESS = {Dordrecht, Holland},
YEAR = {2014},
DATE = {2014},
JOURNAL = {Journal of Automated Reasoning},
VOLUME = {52},
NUMBER = {3},
PAGES = {241--273},
}

Endnote

%0 Journal Article
%A Alkassar, Eyad
%A Böhme, Sascha
%A Mehlhorn, Kurt
%A Rizkallah, Christine
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Framework for the Verification of Certifying Computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-3DF3-7
%R 10.1007/s10817-013-9289-2
%7 2013-06-29
%D 2014
%K Computer Science, Logic in Computer Science, cs.LO,Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Formal Languages and Automata Theory, cs.FL
%J Journal of Automated Reasoning
%V 52
%N 3
%& 241
%P 241 - 273
%I Springer
%C Dordrecht, Holland
%@ false

[84]

S. Bhattacharya, P. Chalermsook, K. Mehlhorn, and A. Neumann, “New Approximability Results for the Robust k-Median Problem,” in Algorithm Theory -- SWAT 2014, Copenhagen, Denmark, 2014.

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BibTeX

@inproceedings{DBLP:conf/swat/BhattacharyaCMN14,
TITLE = {New Approximability Results for the Robust k-Median Problem},
AUTHOR = {Bhattacharya, Sayan and Chalermsook, Parinya and Mehlhorn, Kurt and Neumann, Adrian},
LANGUAGE = {eng},
ISBN = {978-3-319-08403-9},
DOI = {10.1007/978-3-319-08404-6_5},
PUBLISHER = {Springer},
YEAR = {2014},
DATE = {2014},
BOOKTITLE = {Algorithm Theory -- SWAT 2014},
EDITOR = {G{\o}rtz, Inge Li and Ravi, R.},
PAGES = {50--61},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {8503},
ADDRESS = {Copenhagen, Denmark},
}

Endnote

%0 Conference Proceedings
%A Bhattacharya, Sayan
%A Chalermsook, Parinya
%A Mehlhorn, Kurt
%A Neumann, Adrian
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New Approximability Results for the Robust k-Median Problem :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-447B-6
%R 10.1007/978-3-319-08404-6_5
%D 2014
%B 14th Scandinavian Symposium and Workshops on Algorithm Theory
%Z date of event: 2014-07-02 - 2014-07-04
%C Copenhagen, Denmark
%B Algorithm Theory -- SWAT 2014
%E Gørtz, Inge Li; Ravi, R.
%P 50 - 61
%I Springer
%@ 978-3-319-08403-9
%B Lecture Notes in Computer Science
%N 8503

[85]

G. Christodoulou, K. Mehlhorn, and E. Pyrga, “Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms,” Algorithmica, vol. 69, no. 3, 2014.

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BibTeX

@article{DBLP:journals/algorithmica/ChristodoulouMP14,
TITLE = {Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms},
AUTHOR = {Christodoulou, George and Mehlhorn, Kurt and Pyrga, Evangelia},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-013-9753-8},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York, NY},
YEAR = {2014},
DATE = {2014},
JOURNAL = {Algorithmica},
VOLUME = {69},
NUMBER = {3},
PAGES = {619--640},
}

Endnote

%0 Journal Article
%A Christodoulou, George
%A Mehlhorn, Kurt
%A Pyrga, Evangelia
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E27-D
%R 10.1007/s00453-013-9753-8
%7 2013-02-15
%D 2014
%J Algorithmica
%V 69
%N 3
%& 619
%P 619 - 640
%I Springer-Verlag
%C New York, NY
%@ false

[86]

M. Dietzfelbinger, K. Mehlhorn, and P. Sanders, Algorithmen und Datenstrukturen : die Grundwerkzeuge. Berlin: Springer Vieweg, 2014.

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BibTeX

@book{DBLP:journals/jsc/MehlhornSW15,
TITLE = {Algorithmen und Datenstrukturen : die Grundwerkzeuge},
AUTHOR = {Dietzfelbinger, Martin and Mehlhorn, Kurt and Sanders, Peter},
LANGUAGE = {eng},
ISBN = {978-3-642-05472-3},
DOI = {10.1007/978-3-642-05472-3_1},
PUBLISHER = {Springer Vieweg},
ADDRESS = {Berlin},
YEAR = {2014},
DATE = {2014},
PAGES = {XII, 380 p.},
SERIES = {eXamen press},
}

Endnote

%0 Book
%A Dietzfelbinger, Martin
%A Mehlhorn, Kurt
%A Sanders, Peter
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Algorithmen und Datenstrukturen : die Grundwerkzeuge :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E17-2
%@ 978-3-642-05472-3
%R 10.1007/978-3-642-05472-3_1
%I Springer Vieweg
%C Berlin
%D 2014
%P XII, 380 p.
%B eXamen press

[87]

K. Elbassioni, K. Makino, K. Mehlhorn, and F. Ramezani, “On Randomized Fictitious Play for Approximating Saddle Points Over Convex Sets,” 2014. [Online]. Available: http://arxiv.org/abs/1301.5290. (arXiv: 1301.5290)

Abstract

Given two bounded convex sets $X\subseteq\RR^m$ and $Y\subseteq\RR^n,$
specified by membership oracles, and a continuous convex-concave function
$F:X\times Y\to\RR$, we consider the problem of computing an $\eps$-approximate
saddle point, that is, a pair $(x^*,y^*)\in X\times Y$ such that $\sup_{y\in Y}
F(x^*,y)\le \inf_{x\in
X}F(x,y^*)+\eps.$ Grigoriadis and Khachiyan (1995) gave a simple randomized
variant of fictitious play for computing an $\eps$-approximate saddle point for
matrix games, that is, when $F$ is bilinear and the sets $X$ and $Y$ are
simplices. In this paper, we extend their method to the general case. In
particular, we show that, for functions of constant "width", an
$\eps$-approximate saddle point can be computed using
$O^*(\frac{(n+m)}{\eps^2}\ln R)$ random samples from log-concave distributions
over the convex sets $X$ and $Y$. It is assumed that $X$ and $Y$ have inscribed
balls of radius $1/R$ and circumscribing balls of radius $R$. As a consequence,
we obtain a simple randomized polynomial-time algorithm that computes such an
approximation faster than known methods for problems with bounded width and
when $\eps \in (0,1)$ is a fixed, but arbitrarily small constant. Our main tool
for achieving this result is the combination of the randomized fictitious play
with the recently developed results on sampling from convex sets.

Export

BibTeX

@online{DBLP:journals/corr/abs-1301-5290,
TITLE = {On Randomized Fictitious Play for Approximating Saddle Points Over Convex Sets},
AUTHOR = {Elbassioni, Khaled and Makino, Kazuhisa and Mehlhorn, Kurt and Ramezani, Fahimeh},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1301.5290},
EPRINT = {1301.5290},
EPRINTTYPE = {arXiv},
YEAR = {2014},
ABSTRACT = {Given two bounded convex sets $X\subseteq\RR^m$ and $Y\subseteq\RR^n,$ specified by membership oracles, and a continuous convex-concave function $F:X\times Y\to\RR$, we consider the problem of computing an $\eps$-approximate saddle point, that is, a pair $(x^*,y^*)\in X\times Y$ such that $\sup_{y\in Y} F(x^*,y)\le \inf_{x\in X}F(x,y^*)+\eps.$ Grigoriadis and Khachiyan (1995) gave a simple randomized variant of fictitious play for computing an $\eps$-approximate saddle point for matrix games, that is, when $F$ is bilinear and the sets $X$ and $Y$ are simplices. In this paper, we extend their method to the general case. In particular, we show that, for functions of constant "width", an $\eps$-approximate saddle point can be computed using $O^*(\frac{(n+m)}{\eps^2}\ln R)$ random samples from log-concave distributions over the convex sets $X$ and $Y$. It is assumed that $X$ and $Y$ have inscribed balls of radius $1/R$ and circumscribing balls of radius $R$. As a consequence, we obtain a simple randomized polynomial-time algorithm that computes such an approximation faster than known methods for problems with bounded width and when $\eps \in (0,1)$ is a fixed, but arbitrarily small constant. Our main tool for achieving this result is the combination of the randomized fictitious play with the recently developed results on sampling from convex sets.},
}

Endnote

%0 Report
%A Elbassioni, Khaled
%A Makino, Kazuhisa
%A Mehlhorn, Kurt
%A Ramezani, Fahimeh
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Randomized Fictitious Play for Approximating Saddle Points Over
Convex Sets :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E4C-C
%U http://arxiv.org/abs/1301.5290
%D 2014
%X Given two bounded convex sets $X\subseteq\RR^m$ and $Y\subseteq\RR^n,$
specified by membership oracles, and a continuous convex-concave function
$F:X\times Y\to\RR$, we consider the problem of computing an $\eps$-approximate
saddle point, that is, a pair $(x^*,y^*)\in X\times Y$ such that $\sup_{y\in Y}
F(x^*,y)\le \inf_{x\in
X}F(x,y^*)+\eps.$ Grigoriadis and Khachiyan (1995) gave a simple randomized
variant of fictitious play for computing an $\eps$-approximate saddle point for
matrix games, that is, when $F$ is bilinear and the sets $X$ and $Y$ are
simplices. In this paper, we extend their method to the general case. In
particular, we show that, for functions of constant "width", an
$\eps$-approximate saddle point can be computed using
$O^*(\frac{(n+m)}{\eps^2}\ln R)$ random samples from log-concave distributions
over the convex sets $X$ and $Y$. It is assumed that $X$ and $Y$ have inscribed
balls of radius $1/R$ and circumscribing balls of radius $R$. As a consequence,
we obtain a simple randomized polynomial-time algorithm that computes such an
approximation faster than known methods for problems with bounded width and
when $\eps \in (0,1)$ is a fixed, but arbitrarily small constant. Our main tool
for achieving this result is the combination of the randomized fictitious play
with the recently developed results on sampling from convex sets.
%K Computer Science, Computer Science and Game Theory, cs.GT,Mathematics, Optimization and Control, math.OC

[88]

K. Elbassioni, K. Mehlhorn, and F. Ramezani, “Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design,” 2014. [Online]. Available: http://arxiv.org/abs/1408.1577. (arXiv: 1408.1577)

Abstract

R. Lavy and C. Swamy (FOCS 2005, J. ACM 2011) introduced a general method for
obtaining truthful-in-expectation mechanisms from linear programming based
approximation algorithms. Due to the use of the Ellipsoid method, a direct
implementation of the method is unlikely to be efficient in practice. We
propose to use the much simpler and usually faster multiplicative weights
update method instead. The simplification comes at the cost of slightly weaker
approximation and truthfulness guarantees.

Export

BibTeX

@online{DBLP:journals/corr/ElbassioniMR14,
TITLE = {Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design},
AUTHOR = {Elbassioni, Khaled and Mehlhorn, Kurt and Ramezani, Fahimeh},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1408.1577},
EPRINT = {1408.1577},
EPRINTTYPE = {arXiv},
YEAR = {2014},
ABSTRACT = {R. Lavy and C. Swamy (FOCS 2005, J. ACM 2011) introduced a general method for obtaining truthful-in-expectation mechanisms from linear programming based approximation algorithms. Due to the use of the Ellipsoid method, a direct implementation of the method is unlikely to be efficient in practice. We propose to use the much simpler and usually faster multiplicative weights update method instead. The simplification comes at the cost of slightly weaker approximation and truthfulness guarantees.},
}

Endnote

%0 Report
%A Elbassioni, Khaled
%A Mehlhorn, Kurt
%A Ramezani, Fahimeh
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Towards More Practical Linear Programming-based Techniques for Algorithmic Mechanism Design :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-490A-B
%U http://arxiv.org/abs/1408.1577
%D 2014
%8 07.08.2014
%X R. Lavy and C. Swamy (FOCS 2005, J. ACM 2011) introduced a general method for
obtaining truthful-in-expectation mechanisms from linear programming based
approximation algorithms. Due to the use of the Ellipsoid method, a direct
implementation of the method is unlikely to be efficient in practice. We
propose to use the much simpler and usually faster multiplicative weights
update method instead. The simplification comes at the cost of slightly weaker
approximation and truthfulness guarantees.
%K Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Data Structures and Algorithms, cs.DS

[89]

T. Jurkiewicz and K. Mehlhorn, “On a Model of Virtual Address Translation,” Journal of Experimental Algorithmics, vol. 19, 2014.

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BibTeX

@article{JurkiewiczJEA2014,
TITLE = {On a Model of Virtual Address Translation},
AUTHOR = {Jurkiewicz, Tomasz and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1084-6654},
DOI = {10.1145/2656337},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2014},
DATE = {2014},
JOURNAL = {Journal of Experimental Algorithmics},
VOLUME = {19},
PAGES = {1--28},
EID = {1.9},
}

Endnote

%0 Journal Article
%A Jurkiewicz, Tomasz
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On a Model of Virtual Address Translation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-E593-C
%R 10.1145/2656337
%7 2014
%D 2014
%J Journal of Experimental Algorithmics
%O JEA J. Exp. Algorithmics
%V 19
%& 1
%P 1 - 28
%Z sequence number: 1.9
%I ACM
%C New York, NY
%@ false

[90]

T. Jurkiewicz, K. Mehlhorn, and P. Nicholson, “Cache-Oblivious VAT-Algorithms,” 2014. [Online]. Available: http://arxiv.org/abs/1404.3577. (arXiv: 1404.3577)

Abstract

The VAT-model (virtual address translation model) extends the EM-model
(external memory model) and takes the cost of address translation in virtual
memories into account. In this model, the cost of a single memory access may be
logarithmic in the largest address used. We show that the VAT-cost of
cache-oblivious algorithms is only by a constant factor larger than their
EM-cost; this requires a somewhat more stringent tall cache assumption as for
the EM-model.

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BibTeX

@online{JurkiewiczMehlhornNicholson2014,
TITLE = {Cache-Oblivious {VAT}-Algorithms},
AUTHOR = {Jurkiewicz, Tomasz and Mehlhorn, Kurt and Nicholson, Patrick},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1404.3577},
EPRINT = {1404.3577},
EPRINTTYPE = {arXiv},
YEAR = {2014},
ABSTRACT = {The VAT-model (virtual address translation model) extends the EM-model (external memory model) and takes the cost of address translation in virtual memories into account. In this model, the cost of a single memory access may be logarithmic in the largest address used. We show that the VAT-cost of cache-oblivious algorithms is only by a constant factor larger than their EM-cost; this requires a somewhat more stringent tall cache assumption as for the EM-model.},
}

Endnote

%0 Report
%A Jurkiewicz, Tomasz
%A Mehlhorn, Kurt
%A Nicholson, Patrick
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Cache-Oblivious VAT-Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-36C2-4
%U http://arxiv.org/abs/1404.3577
%D 2014
%8 14.01.2014
%X The VAT-model (virtual address translation model) extends the EM-model
(external memory model) and takes the cost of address translation in virtual
memories into account. In this model, the cost of a single memory access may be
logarithmic in the largest address used. We show that the VAT-cost of
cache-oblivious algorithms is only by a constant factor larger than their
EM-cost; this requires a somewhat more stringent tall cache assumption as for
the EM-model.
%K Computer Science, Data Structures and Algorithms, cs.DS

[91]

N. Megiddo, K. Mehlhorn, R. Savani, and V. V. Vazirani, Eds., Equilibrium Computation, no. 8. Schloss Dagstuhl, 2014.

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BibTeX

@proceedings{DBLP:journals/dagstuhl-reports/MegiddoMSV14,
TITLE = {Equilibrium Computation},
EDITOR = {Megiddo, Nimrod and Mehlhorn, Kurt and Savani, Rahul and Vazirani, Vijay V.},
LANGUAGE = {eng},
ISSN = {2192-5283},
URL = {urn:nbn:de:0030-drops-47990},
DOI = {10.4230/DagRep.4.8.73},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2014},
PAGES = {16 p.},
SERIES = {Dagstuhl Reports},
VOLUME = {4},
ISSUE = {8},
ADDRESS = {Wadern, Germany},
}

Endnote

%0 Conference Proceedings
%E Megiddo, Nimrod
%E Mehlhorn, Kurt
%E Savani, Rahul
%E Vazirani, Vijay V.
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Equilibrium Computation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E35-D
%R 10.4230/DagRep.4.8.73
%U urn:nbn:de:0030-drops-47990
%I Schloss Dagstuhl
%D 2014
%8 09.12.2014
%B Dagstuhl Seminar 14342 “Equilibrium Computation"
%Z date of event: 2014-08-17 - 2014-08-22
%D 2014
%C Wadern, Germany
%P 16 p.
%S Dagstuhl Reports
%V 4
%P 73 - 88
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2014/4799/

[92]

K. Mehlhorn, “Algorithms for Equilibrium Prices in Linear Market Models,” in Algorithms and Computation (WALCOM 2014), Chennai, India, 2014.

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BibTeX

@inproceedings{DBLP:conf/walcom/Mehlhorn14,
TITLE = {Algorithms for Equilibrium Prices in Linear Market Models},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-319-04656-3},
DOI = {10.1007/978-3-319-04657-0_1},
PUBLISHER = {Springer},
YEAR = {2014},
DATE = {2014},
BOOKTITLE = {Algorithms and Computation (WALCOM 2014)},
EDITOR = {Pal, Sudebkumar Prasant and Sadakane, Kunihiko},
PAGES = {1--4},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {8344},
ADDRESS = {Chennai, India},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Algorithms for Equilibrium Prices in Linear Market Models :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-4ACF-9
%R 10.1007/978-3-319-04657-0_1
%D 2014
%B 8th International Workshop on Algorithms and Computation
%Z date of event: 2014-02-13 - 2014-02-15
%C Chennai, India
%B Algorithms and Computation
%E Pal, Sudebkumar Prasant; Sadakane, Kunihiko
%P 1 - 4
%I Springer
%@ 978-3-319-04656-3
%B Lecture Notes in Computer Science
%N 8344

[93]

L. Noschinski, C. Rizkallah, and K. Mehlhorn, “Verification of Certifying Computations through AutoCorres and Simpl,” in NASA Formal Methods (NFM 2014), Houston, TX, USA, 2014.

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BibTeX

@inproceedings{DBLP:conf/nfm/NoschinskiRM14,
TITLE = {Verification of Certifying Computations through {AutoCorres} and {Simpl}},
AUTHOR = {Noschinski, Lars and Rizkallah, Christine and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-319-06199-3},
DOI = {10.1007/978-3-319-06200-6_4},
PUBLISHER = {Springer},
YEAR = {2014},
DATE = {2014},
BOOKTITLE = {NASA Formal Methods (NFM 2014)},
EDITOR = {Badger, Julia M. and Rozier, Kristin Yvonne},
PAGES = {46--61},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {8430},
ADDRESS = {Houston, TX, USA},
}

Endnote

%0 Conference Proceedings
%A Noschinski, Lars
%A Rizkallah, Christine
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Verification of Certifying Computations through AutoCorres and Simpl :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5B03-4
%R 10.1007/978-3-319-06200-6_4
%D 2014
%B Sixth NASA Formal Methods Symposium
%Z date of event: 2014-04-29 - 2014-05-01
%C Houston, TX, USA
%B NASA Formal Methods
%E Badger, Julia M.; Rozier, Kristin Yvonne
%P 46 - 61
%I Springer
%@ 978-3-319-06199-3
%B Lecture Notes in Computer Science
%N 8430

2013

[94]

P. Afshani, M. Agrawal, B. Doerr, C. Doerr, K. G. Larsen, and K. Mehlhorn, “The Query Complexity of Finding a Hidden Permutation,” in Space-Efficient Data Structures, Streams, and Algorithms, Berlin: Springer, 2013.

Export

BibTeX

@incollection{Afshani2013,
TITLE = {The Query Complexity of Finding a Hidden Permutation},
AUTHOR = {Afshani, Peyman and Agrawal, Manindra and Doerr, Benjamin and Doerr, Carola and Larsen, Kasper Green and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-642-40272-2},
DOI = {10.1007/978-3-642-40273-9_1},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2013},
DATE = {2013},
BOOKTITLE = {Space-Efficient Data Structures, Streams, and Algorithms},
EDITOR = {Brodnik, Andrej and L{\'o}pez-Ortiz, Alejandro and Raman, Venkatesh and Viola, Alfredo},
PAGES = {1--11},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {8066},
}

Endnote

%0 Book Section
%A Afshani, Peyman
%A Agrawal, Manindra
%A Doerr, Benjamin
%A Doerr, Carola
%A Larsen, Kasper Green
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Query Complexity of Finding a Hidden Permutation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0015-3AC3-A
%F OTHER: Local_ID: 20EA14F7E5BB5FE7C1257C53007A351B-Afshani2013
%R 10.1007/978-3-642-40273-9_1
%D 2013
%B Space-Efficient Data Structures, Streams, and Algorithms
%E Brodnik, Andrej; López-Ortiz, Alejandro; Raman, Venkatesh; Viola, Alfredo
%P 1 - 11
%I Springer
%C Berlin
%@ 978-3-642-40272-2
%S Lecture Notes in Computer Science
%N 8066

[95]

E. Alkassar, S. Böhme, K. Mehlhorn, and C. Rizkallah, “A Framework for the Verification of Certifying Computations,” 2013. [Online]. Available: http://arxiv.org/abs/1301.7462. (arXiv: 1301.7462)

Abstract

Formal verification of complex algorithms is challenging. Verifying their
implementations goes beyond the state of the art of current automatic
verification tools and usually involves intricate mathematical theorems.
Certifying algorithms compute in addition to each output a witness certifying
that the output is correct. A checker for such a witness is usually much
simpler than the original algorithm - yet it is all the user has to trust. The
verification of checkers is feasible with current tools and leads to
computations that can be completely trusted. We describe a framework to
seamlessly verify certifying computations. We use the automatic verifier VCC
for establishing the correctness of the checker and the interactive theorem
prover Isabelle/HOL for high-level mathematical properties of algorithms. We
demonstrate the effectiveness of our approach by presenting the verification of
typical examples of the industrial-level and widespread algorithmic library
LEDA.

Export

BibTeX

@online{AlkassarBohme_arXiv2013,
TITLE = {A Framework for the Verification of Certifying Computations},
AUTHOR = {Alkassar, Eyad and B{\"o}hme, Sascha and Mehlhorn, Kurt and Rizkallah, Christine},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1301.7462},
EPRINT = {1301.7462},
EPRINTTYPE = {arXiv},
YEAR = {2013},
ABSTRACT = {Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms compute in addition to each output a witness certifying that the output is correct. A checker for such a witness is usually much simpler than the original algorithm -- yet it is all the user has to trust. The verification of checkers is feasible with current tools and leads to computations that can be completely trusted. We describe a framework to seamlessly verify certifying computations. We use the automatic verifier VCC for establishing the correctness of the checker and the interactive theorem prover Isabelle/HOL for high-level mathematical properties of algorithms. We demonstrate the effectiveness of our approach by presenting the verification of typical examples of the industrial-level and widespread algorithmic library LEDA.},
}

Endnote

%0 Report
%A Alkassar, Eyad
%A Böhme, Sascha
%A Mehlhorn, Kurt
%A Rizkallah, Christine
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Framework for the Verification of Certifying Computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-3DF0-D
%U http://arxiv.org/abs/1301.7462
%D 2013
%8 30.01.2013
%X Formal verification of complex algorithms is challenging. Verifying their
implementations goes beyond the state of the art of current automatic
verification tools and usually involves intricate mathematical theorems.
Certifying algorithms compute in addition to each output a witness certifying
that the output is correct. A checker for such a witness is usually much
simpler than the original algorithm - yet it is all the user has to trust. The
verification of checkers is feasible with current tools and leads to
computations that can be completely trusted. We describe a framework to
seamlessly verify certifying computations. We use the automatic verifier VCC
for establishing the correctness of the checker and the interactive theorem
prover Isabelle/HOL for high-level mathematical properties of algorithms. We
demonstrate the effectiveness of our approach by presenting the verification of
typical examples of the industrial-level and widespread algorithmic library
LEDA.
%K Computer Science, Logic in Computer Science, cs.LO,Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Formal Languages and Automata Theory, cs.FL

[96]

L. Becchetti, V. Bonifaci, M. Dirnberger, A. Karrenbauer, and K. Mehlhorn, “Physarum Can Compute Shortest Paths: Convergence Proofs and Complexity Bounds,” in Automata, Languages, and Programming (ICALP 2013), Riga, Latvia, 2013.

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BibTeX

@inproceedings{BBDKK2013,
TITLE = {Physarum Can Compute Shortest Paths: {Convergence} Proofs and Complexity Bounds},
AUTHOR = {Becchetti, Luca and Bonifaci, Vincenzo and Dirnberger, Michael and Karrenbauer, Andreas and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-642-39211-5},
DOI = {10.1007/978-3-642-39212-2_42},
PUBLISHER = {Springer},
YEAR = {2013},
DATE = {2013},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2013)},
EDITOR = {Fomin, Fedor V. and Freivalds, R{\=u}si{\c n}{\v s} and Kwiatkowska, Marta and Peleg, David},
PAGES = {472--483},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7966},
ADDRESS = {Riga, Latvia},
}

Endnote

%0 Conference Proceedings
%A Becchetti, Luca
%A Bonifaci, Vincenzo
%A Dirnberger, Michael
%A Karrenbauer, Andreas
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Physarum Can Compute Shortest Paths: Convergence Proofs and Complexity Bounds :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-43EA-3
%R 10.1007/978-3-642-39212-2_42
%D 2013
%B 40th International Colloquium on Automata, Languages and Programming
%Z date of event: 2013-07-08 - 2013-07-12
%C Riga, Latvia
%B Automata, Languages, and Programming
%E Fomin, Fedor V.; Freivalds, Rūsiņš; Kwiatkowska, Marta; Peleg, David
%P 472 - 483
%I Springer
%@ 978-3-642-39211-5
%B Lecture Notes in Computer Science
%N 7966

[97]

S. Bhattacharya, P. Chalermsook, K. Mehlhorn, and A. Neumann, “New Approximability Results for the Robust k-Median Problem,” 2013. [Online]. Available: http://arxiv.org/abs/1309.4602. (arXiv: 1309.4602)

Abstract

We consider a robust variant of the classical $k$-median problem, introduced
by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem},
we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i
\subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$
facilities such that the worst case connection cost over all client sets is
minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony
et al.\ showed an $O(\log m)$ approximation algorithm for any metric and
APX-hardness even in the case of uniform metric. In this paper, we show that
their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$
approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf
DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line
metrics. To our knowledge, this is one of the rare cases in which a problem on
a line metric is hard to approximate to within logarithmic factor. We
complement the hardness result by an experimental evaluation of different
heuristics that shows that very simple heuristics achieve good approximations
for realistic classes of instances.

Export

BibTeX

@online{DBLP:journals/corr/BhattacharyaCMN13,
TITLE = {New Approximability Results for the Robust k-Median Problem},
AUTHOR = {Bhattacharya, Sayan and Chalermsook, Parinya and Mehlhorn, Kurt and Neumann, Adrian},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1309.4602},
EPRINT = {1309.4602},
EPRINTTYPE = {arXiv},
YEAR = {2013},
ABSTRACT = {We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i \subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$ facilities such that the worst case connection cost over all client sets is minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony et al.\ showed an $O(\log m)$ approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$ approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.},
}

Endnote

%0 Report
%A Bhattacharya, Sayan
%A Chalermsook, Parinya
%A Mehlhorn, Kurt
%A Neumann, Adrian
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New Approximability Results for the Robust k-Median Problem :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E4F-6
%U http://arxiv.org/abs/1309.4602
%D 2013
%X We consider a robust variant of the classical $k$-median problem, introduced
by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem},
we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i
\subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$
facilities such that the worst case connection cost over all client sets is
minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony
et al.\ showed an $O(\log m)$ approximation algorithm for any metric and
APX-hardness even in the case of uniform metric. In this paper, we show that
their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$
approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf
DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line
metrics. To our knowledge, this is one of the rare cases in which a problem on
a line metric is hard to approximate to within logarithmic factor. We
complement the hardness result by an experimental evaluation of different
heuristics that shows that very simple heuristics achieve good approximations
for realistic classes of instances.
%K Computer Science, Data Structures and Algorithms, cs.DS

[98]

O. Cheong, K. Mehlhorn, and M. Teillaud, Eds., Computational Geometry, no. 3. Schloss Dagstuhl, 2013.

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BibTeX

@proceedings{DBLP:journals/dagstuhl-reports/CheongMT13,
TITLE = {Computational Geometry},
EDITOR = {Cheong, Otfried and Mehlhorn, Kurt and Teillaud, Monique},
LANGUAGE = {eng},
ISSN = {2192-5283},
URL = {urn:nbn:de:0030-drops-40210},
DOI = {10.4230/DagRep.3.3.1},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2013},
SERIES = {Dagstuhl Reports},
VOLUME = {3},
ISSUE = {3},
PAGES = {1--23},
ADDRESS = {Wadern, Germany},
}

Endnote

%0 Conference Proceedings
%E Cheong, Otfried
%E Mehlhorn, Kurt
%E Teillaud, Monique
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Computational Geometry :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E6A-6
%R 10.4230/DagRep.3.3.1
%U urn:nbn:de:0030-drops-40210
%I Schloss Dagstuhl
%D 2013
%8 04.07.2013
%B Dagstuhl Seminar 13101 "Computational Geometry"
%Z date of event: 2013-03-03 - 2013-03-08
%D 2013
%C Wadern, Germany
%S Dagstuhl Reports
%V 3
%P 1 - 23
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2013/4021/

[99]

G. Christodoulou, K. Mehlhorn, and E. Pyrga, “Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms,” 2013. [Online]. Available: http://arxiv.org/abs/1202.2877. (arXiv: 1202.2877)

Abstract

We reconsider the well-studied Selfish Routing game with affine latency
functions. The Price of Anarchy for this class of games takes maximum value
4/3; this maximum is attained already for a simple network of two parallel
links, known as Pigou's network. We improve upon the value 4/3 by means of
Coordination Mechanisms.
We increase the latency functions of the edges in the network, i.e., if
$\ell_e(x)$ is the latency function of an edge $e$, we replace it by
$\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an
adversary fixes a demand rate as input. The engineered Price of Anarchy of the
mechanism is defined as the worst-case ratio of the Nash social cost in the
modified network over the optimal social cost in the original network.
Formally, if $\CM(r)$ denotes the cost of the worst Nash flow in the modified
network for rate $r$ and $\Copt(r)$ denotes the cost of the optimal flow in the
original network for the same rate then [\ePoA = \max_{r \ge 0}
\frac{\CM(r)}{\Copt(r)}.]
We first exhibit a simple coordination mechanism that achieves for any
network of parallel links an engineered Price of Anarchy strictly less than
4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25.
Then, for the case of two parallel links, we describe an optimal mechanism; its
engineered Price of Anarchy lies between 1.191 and 1.192.

Export

BibTeX

@online{Kurtprice2013,
TITLE = {Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms},
AUTHOR = {Christodoulou, George and Mehlhorn, Kurt and Pyrga, Evangelia},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1202.2877},
EPRINT = {1202.2877},
EPRINTTYPE = {arXiv},
YEAR = {2013},
ABSTRACT = {We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if $\CM(r)$ denotes the cost of the worst Nash flow in the modified network for rate $r$ and $\Copt(r)$ denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.},
}

Endnote

%0 Report
%A Christodoulou, George
%A Mehlhorn, Kurt
%A Pyrga, Evangelia
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A61F-A
%U http://arxiv.org/abs/1202.2877
%D 2013
%8 08.01.2013
%X We reconsider the well-studied Selfish Routing game with affine latency
functions. The Price of Anarchy for this class of games takes maximum value
4/3; this maximum is attained already for a simple network of two parallel
links, known as Pigou's network. We improve upon the value 4/3 by means of
Coordination Mechanisms.
We increase the latency functions of the edges in the network, i.e., if
$\ell_e(x)$ is the latency function of an edge $e$, we replace it by
$\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an
adversary fixes a demand rate as input. The engineered Price of Anarchy of the
mechanism is defined as the worst-case ratio of the Nash social cost in the
modified network over the optimal social cost in the original network.
Formally, if $\CM(r)$ denotes the cost of the worst Nash flow in the modified
network for rate $r$ and $\Copt(r)$ denotes the cost of the optimal flow in the
original network for the same rate then [\ePoA = \max_{r \ge 0}
\frac{\CM(r)}{\Copt(r)}.]
We first exhibit a simple coordination mechanism that achieves for any
network of parallel links an engineered Price of Anarchy strictly less than
4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25.
Then, for the case of two parallel links, we describe an optimal mechanism; its
engineered Price of Anarchy lies between 1.191 and 1.192.
%K Computer Science, Computer Science and Game Theory, cs.GT

[100]

R. Duan and K. Mehlhorn, “A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market,” 2013. [Online]. Available: http://arxiv.org/abs/1212.0979. (arXiv: 1212.0979)

Abstract

We present the first combinatorial polynomial time algorithm for computing
the equilibrium of the Arrow-Debreu market model with linear utilities.

Export

BibTeX

@online{DK2012,
TITLE = {A Combinatorial Polynomial Algorithm for the Linear {Arrow-Debreu} Market},
AUTHOR = {Duan, Ran and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1212.0979},
EPRINT = {1212.0979},
EPRINTTYPE = {arXiv},
LOCALID = {Local-ID: D07870B186956D01C1257AE8000EA12F-DK2012},
YEAR = {2013},
ABSTRACT = {We present the first combinatorial polynomial time algorithm for computing the equilibrium of the Arrow-Debreu market model with linear utilities.},
}

Endnote

%0 Report
%A Duan, Ran
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-F74C-E
%U http://arxiv.org/abs/1212.0979
%F OTHER: Local-ID: D07870B186956D01C1257AE8000EA12F-DK2012
%D 2013
%8 13.09.2013
%X We present the first combinatorial polynomial time algorithm for computing
the equilibrium of the Arrow-Debreu market model with linear utilities.
%K Computer Science, Data Structures and Algorithms, cs.DS

[101]

R. Duan and K. Mehlhorn, “A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market,” in Automata, Languages, and Programming (ICALP 2013), Riga, Latvia, 2013.

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BibTeX

@inproceedings{DBLP:conf/icalp/DuanM13,
TITLE = {A Combinatorial Polynomial Algorithm for the Linear {Arrow}-{Debreu} Market},
AUTHOR = {Duan, Ran and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-642-39205-4},
DOI = {10.1007/978-3-642-39206-1_36},
PUBLISHER = {Springer},
YEAR = {2014},
DATE = {2013},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2013)},
EDITOR = {Fomin, Fedor V. and Freivalds, R{\=u}si{\c n}{\v s} and Kwiatkowska, Marta and Peleg, David},
PAGES = {425--436},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7965},
ADDRESS = {Riga, Latvia},
}

Endnote

%0 Conference Proceedings
%A Duan, Ran
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Combinatorial Polynomial Algorithm for the Linear Arrow-Debreu Market :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E4A-0
%R 10.1007/978-3-642-39206-1_36
%D 2013
%B 40th International Colloquium on Automata, Languages and Programming,
%Z date of event: 2014-07-08 - 2014-07-12
%C Riga, Latvia
%B Automata, Languages, and Programming
%E Fomin, Fedor V.; Freivalds, Rūsiņš; Kwiatkowska , Marta; Peleg, David
%P 425 - 436
%I Springer
%@ 978-3-642-39205-4
%B Lecture Notes in Computer Science
%N 7965

[102]

K. Elbassioni, K. Makino, K. Mehlhorn, and F. Ramezani, “On Randomized Fictitious Play for Approximating Saddle Points over Convex Sets,” in Computing and Combinatorics (COCOON 2013), Hangzhou, China, 2013.

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BibTeX

@inproceedings{Ramezani2013,
TITLE = {On Randomized Fictitious Play for Approximating Saddle Points over Convex Sets},
AUTHOR = {Elbassioni, Khaled and Makino, Kazuhisa and Mehlhorn, Kurt and Ramezani, Fahimeh},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-38767-8},
DOI = {10.1007/978-3-642-38768-5_8},
LOCALID = {Local-ID: 462364EE2334C4A9C1257C60005317D1-Ramezani2013},
PUBLISHER = {Springer},
YEAR = {2013},
DATE = {2013},
BOOKTITLE = {Computing and Combinatorics (COCOON 2013)},
EDITOR = {Du, Ding-Zhu and Zhang, Guochuan},
PAGES = {65--76},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7636},
ADDRESS = {Hangzhou, China},
}

Endnote

%0 Conference Proceedings
%A Elbassioni, Khaled
%A Makino, Kazuhisa
%A Mehlhorn, Kurt
%A Ramezani, Fahimeh
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T On Randomized Fictitious Play for Approximating Saddle Points over Convex Sets :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0015-7905-0
%F OTHER: Local-ID: 462364EE2334C4A9C1257C60005317D1-Ramezani2013
%R 10.1007/978-3-642-38768-5_8
%D 2013
%B 19th International Conference on Computing and Combinatorics
%Z date of event: 2013-06-21 - 2013-06-23
%C Hangzhou, China
%B Computing and Combinatorics
%E Du, Ding-Zhu; Zhang, Guochuan
%P 65 - 76
%I Springer
%@ 978-3-642-38767-8
%B Lecture Notes in Computer Science
%N 7636
%@ false

[103]

A. Elmasry, K. Mehlhorn, and J. M. Schmidt, “Every DFS Tree of a 3-connected Graph Contains a Contractible Edge,” Journal of Graph Theory, vol. 72, no. 1, 2013.

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BibTeX

@article{Elmasry2013,
TITLE = {Every {DFS} Tree of a 3-connected Graph Contains a Contractible Edge},
AUTHOR = {Elmasry, Amr and Mehlhorn, Kurt and Schmidt, Jens M.},
LANGUAGE = {eng},
ISSN = {0364-9024},
DOI = {10.1002/jgt.21635},
LOCALID = {Local-ID: 4FE50A6D333665B3C1257AC200498D2D-Elmasry2013},
PUBLISHER = {John Wiley \& Sons.},
ADDRESS = {New York},
YEAR = {2013},
DATE = {2013},
JOURNAL = {Journal of Graph Theory},
VOLUME = {72},
NUMBER = {1},
PAGES = {112--121},
}

Endnote

%0 Journal Article
%A Elmasry, Amr
%A Mehlhorn, Kurt
%A Schmidt, Jens M.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Every DFS Tree of a 3-connected Graph Contains a Contractible Edge :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0015-78FA-7
%R 10.1002/jgt.21635
%F OTHER: Local-ID: 4FE50A6D333665B3C1257AC200498D2D-Elmasry2013
%7 2012-03
%D 2013
%J Journal of Graph Theory
%V 72
%N 1
%& 112
%P 112 - 121
%I John Wiley & Sons.
%C New York
%@ false

[104]

C.-C. Huang, T. Kavitha, K. Mehlhorn, and D. Michail, “Fair Matchings and Related Problems,” in 33rd International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013), Guwahati, India, 2013.

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BibTeX

@inproceedings{HuangFSTTCS2013,
TITLE = {Fair Matchings and Related Problems},
AUTHOR = {Huang, Chien-Chung and Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
ISSN = {1868-896},
ISBN = {978-3-939897-64-4},
URL = {urn:nbn:de:0030-drops-43841},
DOI = {10.4230/LIPIcs.FSTTCS.2013.339},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2013},
BOOKTITLE = {33rd International Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
EDITOR = {Seth, Anil and Vishnoi, Nisheeth K.},
PAGES = {339--350},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {24},
ADDRESS = {Guwahati, India},
}

Endnote

%0 Conference Proceedings
%A Huang, Chien-Chung
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Fair Matchings and Related Problems :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E46-7
%R 10.4230/LIPIcs.FSTTCS.2013.339
%U urn:nbn:de:0030-drops-43841
%D 2013
%B 33rd International Conference on Foundations of Software Technology and Theoretical Computer Science
%Z date of event: 2013-12-12 - 2013-12-14
%C Guwahati, India
%B 33rd International Conference on Foundations of Software Technology and Theoretical Computer Science
%E Seth, Anil; Vishnoi, Nisheeth K.
%P 339 - 350
%I Schloss Dagstuhl
%@ 978-3-939897-64-4
%B Leibniz International Proceedings in Informatics
%N 24
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2013/4384/

[105]

T. Jurkiewicz and K. Mehlhorn, “The Cost of Address Translation,” in Proceedings of the 15th Meeting on Algorithm Engineering and Experiments (ALENEX 2013), New Orleans, LA, USA, 2013.

Abstract

Modern computers are not random access machines (RAMs). They have a memory hierarchy, multiple cores, and virtual memory. In this paper, we address the computational cost of address translation in virtual memory. Starting point for our work is the observation that the analysis of some simple algorithms (random scan of an rray, binary search, heapsort) in either the RAM model or the EM model (external memory model) does not correctly predict growth rates of actual running times.
We propose the VAT model (virtual address translation) to account for the cost of address translations and analyze the algorithms mentioned above and others in the model.
The predictions agree with the measurements.
We also analyze the VAT-cost of cache-oblivious algorithms.

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BibTeX

@inproceedings{VAT2013,
TITLE = {The Cost of Address Translation},
AUTHOR = {Jurkiewicz, Tomasz and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-1-61197-253-5},
DOI = {10.1137/1.9781611972931.13},
LOCALID = {Local-ID: 8547751BA6E798C6C1257AD20051B773-VAT2013},
PUBLISHER = {SIAM},
YEAR = {2013},
ABSTRACT = {Modern computers are not random access machines (RAMs). They have a memory hierarchy, multiple cores, and virtual memory. In this paper, we address the computational cost of address translation in virtual memory. Starting point for our work is the observation that the analysis of some simple algorithms (random scan of an rray, binary search, heapsort) in either the RAM model or the EM model (external memory model) does not correctly predict growth rates of actual running times. We propose the VAT model (virtual address translation) to account for the cost of address translations and analyze the algorithms mentioned above and others in the model. The predictions agree with the measurements. We also analyze the VAT-cost of cache-oblivious algorithms.},
BOOKTITLE = {Proceedings of the 15th Meeting on Algorithm Engineering and Experiments (ALENEX 2013)},
EDITOR = {Sanders, Peter and Zeh, Norbert},
PAGES = {148--162},
ADDRESS = {New Orleans, LA, USA},
}

Endnote

%0 Conference Proceedings
%A Jurkiewicz, Tomasz
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Cost of Address Translation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0015-8656-6
%R 10.1137/1.9781611972931.13
%F OTHER: Local-ID: 8547751BA6E798C6C1257AD20051B773-VAT2013
%D 2013
%B 15th Meeting on Algorithm Engineering and Experiments
%Z date of event: 2013-01-07 - 2013-01-07
%C New Orleans, LA, USA
%X Modern computers are not random access machines (RAMs). They have a memory hierarchy, multiple cores, and virtual memory. In this paper, we address the computational cost of address translation in virtual memory. Starting point for our work is the observation that the analysis of some simple algorithms (random scan of an rray, binary search, heapsort) in either the RAM model or the EM model (external memory model) does not correctly predict growth rates of actual running times.
We propose the VAT model (virtual address translation) to account for the cost of address translations and analyze the algorithms mentioned above and others in the model.
The predictions agree with the measurements.
We also analyze the VAT-cost of cache-oblivious algorithms.
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,Computer Science, Performance, cs.PF,
%B Proceedings of the 15th Meeting on Algorithm Engineering and Experiments
%E Sanders, Peter; Zeh, Norbert
%P 148 - 162
%I SIAM
%@ 978-1-61197-253-5

[106]

K. Mehlhorn, A. Neumann, and J. M. Schmidt, “Certifying 3-Edge-Connectivity,” 2013. [Online]. Available: http://arxiv.org/abs/1211.6553. (arXiv: 1211.6553)

Abstract

We present a certifying algorithm that tests graphs for 3-edge-connectivity;
the algorithm works in linear time. If the input graph is not 3-edge-connected,
the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a
construction sequence that constructs the input graph from the graph with two
vertices and three parallel edges using only operations that (obviously)
preserve 3-edge-connectivity. Additionally, we show how compute and certify the
3-edge-connected components and a cactus representation of the 2-cuts in linear
time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected
components of a 2-connected graph.

Export

BibTeX

@online{Kurt3edge2013,
TITLE = {Certifying 3-Edge-Connectivity},
AUTHOR = {Mehlhorn, Kurt and Neumann, Adrian and Schmidt, Jens M.},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1211.6553},
EPRINT = {1211.6553},
EPRINTTYPE = {arXiv},
YEAR = {2013},
ABSTRACT = {We present a certifying algorithm that tests graphs for 3-edge-connectivity; the algorithm works in linear time. If the input graph is not 3-edge-connected, the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a construction sequence that constructs the input graph from the graph with two vertices and three parallel edges using only operations that (obviously) preserve 3-edge-connectivity. Additionally, we show how compute and certify the 3-edge-connected components and a cactus representation of the 2-cuts in linear time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected components of a 2-connected graph.},
}

Endnote

%0 Report
%A Mehlhorn, Kurt
%A Neumann, Adrian
%A Schmidt, Jens M.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying 3-Edge-Connectivity :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A622-F
%U http://arxiv.org/abs/1211.6553
%D 2013
%8 04.11.2013
%X We present a certifying algorithm that tests graphs for 3-edge-connectivity;
the algorithm works in linear time. If the input graph is not 3-edge-connected,
the algorithm returns a 2-edge-cut. If it is 3-edge-connected, it returns a
construction sequence that constructs the input graph from the graph with two
vertices and three parallel edges using only operations that (obviously)
preserve 3-edge-connectivity. Additionally, we show how compute and certify the
3-edge-connected components and a cactus representation of the 2-cuts in linear
time. For 3-vertex-connectivity, we show how to compute the 3-vertex-connected
components of a 2-connected graph.
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Discrete Mathematics, cs.DM

[107]

K. Mehlhorn, “Physarum Computations (Invited talk),” in 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), Kiel, Germany, 2013.

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BibTeX

@inproceedings{DBLP:conf/stacs/Mehlhorn13,
TITLE = {Physarum Computations (Invited talk)},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-939897-50-7},
URL = {urn:nbn:de:0030-drops-39166},
DOI = {10.4230/LIPIcs.STACS.2013.5},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2013},
BOOKTITLE = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
EDITOR = {Portier, Natacha and Wilke, Thomas},
PAGES = {5--6},
SERIES = {Leibniz International Proceedings in Informatics},
VOLUME = {20},
ADDRESS = {Kiel, Germany},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Physarum Computations (Invited talk) :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E6E-D
%U urn:nbn:de:0030-drops-39166
%R 10.4230/LIPIcs.STACS.2013.5
%D 2013
%8 18.02.2013
%B 30th International Symposium on Theoretical Aspects of Computer Science
%Z date of event: 2013-02-27 - 2013-03-02
%C Kiel, Germany
%B 30th International Symposium on Theoretical Aspects of Computer Science
%E Portier, Natacha; Wilke, Thomas
%P 5 - 6
%I Schloss Dagstuhl
%@ 978-3-939897-50-7
%B Leibniz International Proceedings in Informatics
%N 20
%U http://drops.dagstuhl.de/opus/volltexte/2013/3916/

[108]

K. Mehlhorn, M. Y. Vardi, and M. Herbstritt, Eds., Publication Culture in Computing Research, no. 11. Schloss Dagstuhl, 2013.

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BibTeX

@proceedings{mehlhorn_et_al:DR:2013:3977,
TITLE = {Publication Culture in Computing Research},
EDITOR = {Mehlhorn, Kurt and Vardi, Moshe Y. and Herbstritt, Marc},
LANGUAGE = {eng},
ISSN = {2192-5283},
URL = {urn:nbn:de:0030-drops-39778},
DOI = {10.4230/DagRep.2.11.20},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2012},
SERIES = {Dagstuhl Reports},
VOLUME = {2},
ISSUE = {11},
PAGES = {20--44},
ADDRESS = {Wadern, Germany},
}

Endnote

%0 Conference Proceedings
%E Mehlhorn, Kurt
%E Vardi, Moshe Y.
%E Herbstritt, Marc
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Publication Culture in Computing Research :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A44B-5
%R 10.4230/DagRep.2.11.20
%U urn:nbn:de:0030-drops-39778
%D 2013
%8 25.03.2013
%B Dagstuhl Perspectives Workshop 12452
%Z date of event: 2012-11-06 - 2012-11-09
%D 2012
%C Wadern, Germany
%K scholarly publishing, conference, journal, peer review, open archive, open access, indexing, research evaluation
%S Dagstuhl Reports
%V 2
%P 20 - 44
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2013/3977/

[109]

K. Mehlhorn, M. Sagraloff, and P. Wang, “From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition,” 2013. [Online]. Available: http://arxiv.org/abs/1301.4870. (arXiv: 1301.4870)

Abstract

We present an algorithm for isolating the roots of an arbitrary complex
polynomial $p$ that also works for polynomials with multiple roots provided
that the number $k$ of distinct roots is given as part of the input. It outputs
$k$ pairwise disjoint disks each containing one of the distinct roots of $p$,
and its multiplicity. The algorithm uses approximate factorization as a
subroutine.
In addition, we apply the new root isolation algorithm to a recent algorithm
for computing the topology of a real planar algebraic curve specified as the
zero set of a bivariate integer polynomial and for isolating the real solutions
of a bivariate polynomial system. For input polynomials of degree $n$ and
bitsize $\tau$, we improve the currently best running time from
$\tO(n^{9}\tau+n^{8}\tau^{2})$ (deterministic) to $\tO(n^{6}+n^{5}\tau)$
(randomized) for topology computation and from $\tO(n^{8}+n^{7}\tau)$
(deterministic) to $\tO(n^{6}+n^{5}\tau)$ (randomized) for solving bivariate
systems.

Export

BibTeX

@online{MSWClustering2013,
TITLE = {From Approximate Factorization to Root Isolation with Application to Cylindrical Algebraic Decomposition},
AUTHOR = {Mehlhorn, Kurt and Sagraloff, Michael and Wang, Pengming},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1301.4870},
EPRINT = {1301.4870},
EPRINTTYPE = {arXiv},
YEAR = {2013},
ABSTRACT = {We present an algorithm for isolating the roots of an arbitrary complex polynomial $p$ that also works for polynomials with multiple roots provided that the number $k$ of distinct roots is given as part of the input. It outputs $k$ pairwise disjoint disks each containing one of the distinct roots of $p$, and its multiplicity. The algorithm uses approximate factorization as a subroutine. In addition, we apply the new root isolation algorithm to a recent algorithm for computing the topology of a real planar algebraic curve specified as the zero set of a bivariate integer polynomial and for isolating the real solutions of a bivariate polynomial system. For input polynomials of degree $n$ and bitsize $\tau$, we improve the currently best running time from $\tO(n^{9}\tau+n^{8}\tau^{2})$ (deterministic) to $\tO(n^{6}+n^{5}\tau)$ (randomized) for topology computation and from $\tO(n^{8}+n^{7}\tau)$ (deterministic) to $\tO(n^{6}+n^{5}\tau)$ (randomized) for solving bivariate systems.},
}

Endnote

%0 Report
%A Mehlhorn, Kurt
%A Sagraloff, Michael
%A Wang, Pengming
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T From Approximate Factorization to Root Isolation with Application to
Cylindrical Algebraic Decomposition :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0018-AB2E-0
%U http://arxiv.org/abs/1301.4870
%D 2013
%X We present an algorithm for isolating the roots of an arbitrary complex
polynomial $p$ that also works for polynomials with multiple roots provided
that the number $k$ of distinct roots is given as part of the input. It outputs
$k$ pairwise disjoint disks each containing one of the distinct roots of $p$,
and its multiplicity. The algorithm uses approximate factorization as a
subroutine.
In addition, we apply the new root isolation algorithm to a recent algorithm
for computing the topology of a real planar algebraic curve specified as the
zero set of a bivariate integer polynomial and for isolating the real solutions
of a bivariate polynomial system. For input polynomials of degree $n$ and
bitsize $\tau$, we improve the currently best running time from
$\tO(n^{9}\tau+n^{8}\tau^{2})$ (deterministic) to $\tO(n^{6}+n^{5}\tau)$
(randomized) for topology computation and from $\tO(n^{8}+n^{7}\tau)$
(deterministic) to $\tO(n^{6}+n^{5}\tau)$ (randomized) for solving bivariate
systems.
%K Computer Science, Symbolic Computation, cs.SC

[110]

K. Mehlhorn, A. Neumann, and J. M. Schmidt, “Certifying 3-Edge-Connectivity,” in Graph-theoretic Concepts in Computer Science (WG 2013), Lübeck, Germany, 2013.

Export

BibTeX

@inproceedings{Mehlhorn2013,
TITLE = {Certifying 3-Edge-Connectivity},
AUTHOR = {Mehlhorn, Kurt and Neumann, Adrian and Schmidt, Jens M.},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-45042-6},
DOI = {10.1007/978-3-642-45043-3_31},
PUBLISHER = {Springer},
YEAR = {2013},
DATE = {2013},
BOOKTITLE = {Graph-theoretic Concepts in Computer Science (WG 2013)},
EDITOR = {Brandst{\"a}dt, Andreas and Jansen, Klaus and Reischuk, R{\"u}diger},
PAGES = {358--369},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {8165},
ADDRESS = {L{\"u}beck, Germany},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Neumann, Adrian
%A Schmidt, Jens M.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying 3-Edge-Connectivity :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0015-3EAD-B
%R 10.1007/978-3-642-45043-3_31
%D 2013
%B 39th International Workshop on Graph-Theoretic Concepts in Computer Science
%Z date of event: 2013-06-19 - 2013-06-21
%C Lübeck, Germany
%B Graph-theoretic Concepts in Computer Science
%E Brandstädt, Andreas; Jansen, Klaus; Reischuk, Rüdiger
%P 358 - 369
%I Springer
%@ 978-3-642-45042-6
%B Lecture Notes in Computer Science
%N 8165
%@ false

[111]

K. Mehlhorn, M. Sagraloff, and P. Wang, “From Approximate Factorization to Root Isolation,” in ISSAC 2013, 38th International Symposium on Symbolic and Algebraic Computation, Boston, MA, USA, 2013.

Export

BibTeX

@inproceedings{DBLP:conf/issac/MehlhornSW13,
TITLE = {From Approximate Factorization to Root Isolation},
AUTHOR = {Mehlhorn, Kurt and Sagraloff, Michael and Wang, Pengming},
LANGUAGE = {eng},
ISBN = {978-1-4503-2059-7},
DOI = {10.1145/2465506.2465523},
PUBLISHER = {ACM},
YEAR = {2013},
DATE = {2013},
BOOKTITLE = {ISSAC 2013, 38th International Symposium on Symbolic and Algebraic Computation},
EDITOR = {Kauers, Manuel},
PAGES = {283--290},
ADDRESS = {Boston, MA, USA},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Sagraloff, Michael
%A Wang, Pengming
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T From Approximate Factorization to Root Isolation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-444D-C
%R 10.1145/2465506.2465523
%D 2013
%B 38th International Symposium on Symbolic and Algebraic Computation
%Z date of event: 2013-06-26 - 2013-06-29
%C Boston, MA, USA
%B ISSAC 2013
%E Kauers, Manuel
%P 283 - 290
%I ACM
%@ 978-1-4503-2059-7

[112]

M. Sagraloff and K. Mehlhorn, “Computing Real Roots of Real Polynomials,” 2013. [Online]. Available: http://arxiv.org/abs/1308.4088. (arXiv: 1308.4088)

Abstract

Computing the real roots of a polynomial is a fundamental problem of
computational algebra. We describe a variant of the Descartes method that
isolates the real roots of any real square-free polynomial given through
coefficient oracles. A coefficient oracle provides arbitrarily good
approximations of the coefficients. The bit complexity of the algorithm matches
the complexity of the best algorithm known, and the algorithm is simpler than
this algorithm. The algorithm derives its speed from the combination of
Descartes method with Newton iteration. Our algorithm can also be used to
further refine the isolating intervals to an arbitrary small size. The
complexity of root refinement is nearly optimal.

Export

BibTeX

@online{DBLP:journals/corr/SagraloffM13,
TITLE = {Computing Real Roots of Real Polynomials},
AUTHOR = {Sagraloff, Michael and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1308.4088},
EPRINT = {1308.4088},
EPRINTTYPE = {arXiv},
YEAR = {2013},
ABSTRACT = {Computing the real roots of a polynomial is a fundamental problem of computational algebra. We describe a variant of the Descartes method that isolates the real roots of any real square-free polynomial given through coefficient oracles. A coefficient oracle provides arbitrarily good approximations of the coefficients. The bit complexity of the algorithm matches the complexity of the best algorithm known, and the algorithm is simpler than this algorithm. The algorithm derives its speed from the combination of Descartes method with Newton iteration. Our algorithm can also be used to further refine the isolating intervals to an arbitrary small size. The complexity of root refinement is nearly optimal.},
}

Endnote

%0 Report
%A Sagraloff, Michael
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Computing Real Roots of Real Polynomials :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-4591-A
%U http://arxiv.org/abs/1308.4088
%D 2013
%X Computing the real roots of a polynomial is a fundamental problem of
computational algebra. We describe a variant of the Descartes method that
isolates the real roots of any real square-free polynomial given through
coefficient oracles. A coefficient oracle provides arbitrarily good
approximations of the coefficients. The bit complexity of the algorithm matches
the complexity of the best algorithm known, and the algorithm is simpler than
this algorithm. The algorithm derives its speed from the combination of
Descartes method with Newton iteration. Our algorithm can also be used to
further refine the isolating intervals to an arbitrary small size. The
complexity of root refinement is nearly optimal.
%K Computer Science, Symbolic Computation, cs.SC,Computer Science, Numerical Analysis, cs.NA,Mathematics, Numerical Analysis, math.NA

2012

[113]

P. Afshani, M. Agrawal, B. Doerr, K. G. Larsen, K. Mehlhorn, and C. Winzen, “The Query Complexity of Finding a Hidden Permutation,” Electronic Colloquium on Computational Complexity (ECCC) : Report Series, vol. 87 (Revision 1), 2012.

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BibTeX

@article{AfshaniADGLMW12eccv,
TITLE = {The Query Complexity of Finding a Hidden Permutation},
AUTHOR = {Afshani, Peyman and Agrawal, Manindra and Doerr, Benjamin and Larsen, Kasper Green and Mehlhorn, Kurt and Winzen, Carola},
LANGUAGE = {eng},
ISSN = {1433-8092},
PUBLISHER = {Hasso-Plattner-Institut f{\"u}r Softwaretechnik GmbH},
ADDRESS = {Potsdam},
YEAR = {2012},
JOURNAL = {Electronic Colloquium on Computational Complexity (ECCC) : Report Series},
VOLUME = {87 (Revision 1)},
PAGES = {1--36},
}

Endnote

%0 Journal Article
%A Afshani, Peyman
%A Agrawal, Manindra
%A Doerr, Benjamin
%A Larsen, Kasper Green
%A Mehlhorn, Kurt
%A Winzen, Carola
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Query Complexity of Finding a Hidden Permutation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0025-0634-2
%7 2012-11-05
%D 2012
%8 05.11.2012
%K Query complexity; randomized algorithms; guessing games; Mastermind
%J Electronic Colloquium on Computational Complexity (ECCC) : Report Series
%O ECCC
%V 87 (Revision 1)
%& 1
%P 1 - 36
%I Hasso-Plattner-Institut für Softwaretechnik GmbH
%C Potsdam
%@ false
%U http://eccc.hpi-web.de/report/2012/087/revision/1/download

[114]

P. Afshani, M. Agrawal, B. Doerr, K. G. Larsen, K. Mehlhorn, and C. Winzen, “The Deterministic and Randomized Query Complexity of a Simple Guessing Game,” Electronic Colloquium on Computational Complexity (ECCC) : Report Series, vol. 87, 2012.

Export

BibTeX

@article{KurtECCC2012,
TITLE = {The Deterministic and Randomized Query Complexity of a Simple Guessing Game},
AUTHOR = {Afshani, Peyman and Agrawal, Manindra and Doerr, Benjamin and Larsen, Kasper Green and Mehlhorn, Kurt and Winzen, Carola},
LANGUAGE = {eng},
ISSN = {1433-8092},
PUBLISHER = {Hasso-Plattner-Institut f{\"u}r Softwaretechnik GmbH},
ADDRESS = {Potsdam},
YEAR = {2012},
JOURNAL = {Electronic Colloquium on Computational Complexity (ECCC) : Report Series},
VOLUME = {87},
PAGES = {1--33},
}

Endnote

%0 Journal Article
%A Afshani, Peyman
%A Agrawal, Manindra
%A Doerr, Benjamin
%A Larsen, Kasper Green
%A Mehlhorn, Kurt
%A Winzen, Carola
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Deterministic and Randomized Query Complexity of a Simple Guessing Game :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A450-8
%7 2012
%D 2012
%K Query complexity; randomized algorithms; guessing games; Mastermind
%J Electronic Colloquium on Computational Complexity (ECCC) : Report Series
%O ECCC
%V 87
%& 1
%P 1 - 33
%I Hasso-Plattner-Institut für Softwaretechnik GmbH
%C Potsdam
%@ false
%U http://eccc.hpi-web.de/report/2012/087/

[115]

V. Bonifaci, K. Mehlhorn, and G. Varma, “Physarum Can Compute Shortest Paths,” in Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012), Kyoto, Japan, 2012.

Abstract

Physarum Polycephalum is a slime mold that is apparently able to solve shortest
path problems.
A mathematical model has been proposed by biologists to describe the feedback
mechanism used by the slime mold to adapt its tubular channels while foraging
two food sources s_0 and s_1. We prove that, under this model, the mass of
the mold will eventually converge to the shortest s_0-s_1 path of the
network that the mold lies on, independently of the structure of the network or
of the initial mass distribution.
This matches the experimental observations by the biologists and can be seen as
an example of a "natural algorithm", that is, an algorithm developed by
evolution over millions of years.

Export

BibTeX

@inproceedings{Bonifaci2012a,
TITLE = {Physarum Can Compute Shortest Paths},
AUTHOR = {Bonifaci, Vincenzo and Mehlhorn, Kurt and Varma, Girish},
LANGUAGE = {eng},
ISBN = {978-1-611972-11-5},
LOCALID = {Local-ID: CA211EE0A1B815F8C1257AC200545CEC-Bonifaci2012a},
PUBLISHER = {SIAM},
YEAR = {2012},
DATE = {2012},
ABSTRACT = {Physarum Polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels while foraging two food sources s_0 and s_1. We prove that, under this model, the mass of the mold will eventually converge to the shortest s_0-s_1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a "natural algorithm", that is, an algorithm developed by evolution over millions of years.},
BOOKTITLE = {Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2012)},
EDITOR = {Ravani, Yuval},
PAGES = {233--240},
ADDRESS = {Kyoto, Japan},
}

Endnote

%0 Conference Proceedings
%A Bonifaci, Vincenzo
%A Mehlhorn, Kurt
%A Varma, Girish
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Physarum Can Compute Shortest Paths :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BB81-8
%F OTHER: Local-ID: CA211EE0A1B815F8C1257AC200545CEC-Bonifaci2012a
%D 2012
%B Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2012-01-17 - 2012-01-19
%C Kyoto, Japan
%X Physarum Polycephalum is a slime mold that is apparently able to solve shortest
path problems.
A mathematical model has been proposed by biologists to describe the feedback
mechanism used by the slime mold to adapt its tubular channels while foraging
two food sources s_0 and s_1. We prove that, under this model, the mass of
the mold will eventually converge to the shortest s_0-s_1 path of the
network that the mold lies on, independently of the structure of the network or
of the initial mass distribution.
This matches the experimental observations by the biologists and can be seen as
an example of a "natural algorithm", that is, an algorithm developed by
evolution over millions of years.
%B Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
%E Ravani, Yuval
%P 233 - 240
%I SIAM
%@ 978-1-611972-11-5

[116]

V. Bonifaci, K. Mehlhorn, and G. Varma, “Physarum Can Compute Shortest Paths,” Journal of Theoretical Biology, vol. 309, 2012.

Abstract

Physarum Polycephalum is a slime mold that is apparently able to solve shortest
path problems.
A mathematical model has been proposed by biologists to describe the feedback
mechanism used by the slime mold to adapt its tubular channels while foraging
two food sources s_0 and s_1. We prove that, under this model, the mass of
the mold will eventually converge to the shortest s_0-s_1 path of the
network that the mold lies on, independently of the structure of the network or
of the initial mass distribution.
This matches the experimental observations by the biologists and can be seen as
an example of a "natural algorithm", that is, an algorithm developed by
evolution over millions of years.

Export

BibTeX

@article{Bonifaci2012c,
TITLE = {Physarum Can Compute Shortest Paths},
AUTHOR = {Bonifaci, Vincenzo and Mehlhorn, Kurt and Varma, Girish},
LANGUAGE = {eng},
ISSN = {0022-5193},
DOI = {10.1016/j.jtbi.2012.06.017},
LOCALID = {Local-ID: 2E63427366C2D939C1257AC2005DC800-Bonifaci2012c},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2012},
DATE = {2012},
ABSTRACT = {Physarum Polycephalum is a slime mold that is apparently able to solve shortest path problems. A mathematical model has been proposed by biologists to describe the feedback mechanism used by the slime mold to adapt its tubular channels while foraging two food sources s_0 and s_1. We prove that, under this model, the mass of the mold will eventually converge to the shortest s_0-s_1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a "natural algorithm", that is, an algorithm developed by evolution over millions of years.},
JOURNAL = {Journal of Theoretical Biology},
VOLUME = {309},
PAGES = {121--133},
}

Endnote

%0 Journal Article
%A Bonifaci, Vincenzo
%A Mehlhorn, Kurt
%A Varma, Girish
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Physarum Can Compute Shortest Paths :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-C4DA-A
%R 10.1016/j.jtbi.2012.06.017
%F OTHER: Local-ID: 2E63427366C2D939C1257AC2005DC800-Bonifaci2012c
%7 2012-06-22
%D 2012
%X Physarum Polycephalum is a slime mold that is apparently able to solve shortest
path problems.
A mathematical model has been proposed by biologists to describe the feedback
mechanism used by the slime mold to adapt its tubular channels while foraging
two food sources s_0 and s_1. We prove that, under this model, the mass of
the mold will eventually converge to the shortest s_0-s_1 path of the
network that the mold lies on, independently of the structure of the network or
of the initial mass distribution.
This matches the experimental observations by the biologists and can be seen as
an example of a "natural algorithm", that is, an algorithm developed by
evolution over millions of years.
%K slime mold, natural algorithm, natural adaptive networks
%J Journal of Theoretical Biology
%V 309
%& 121
%P 121 - 133
%I Elsevier
%C Amsterdam
%@ false

[117]

K. Bringmann, K. Mehlhorn, and A. Neumann, “Remarks on Category-based Routing in Social Networks,” 2012. [Online]. Available: http://arxiv.org/abs/1202.2293. (arXiv: 1202.2293)

Abstract

It is well known that individuals can route messages on short paths through
social networks, given only simple information about the target and using only
local knowledge about the topology. Sociologists conjecture that people find
routes greedily by passing the message to an acquaintance that has more in
common with the target than themselves, e.g. if a dentist in Saarbr\"ucken
wants to send a message to a specific lawyer in Munich, he may forward it to
someone who is a lawyer and/or lives in Munich. Modelling this setting,
Eppstein et al. introduced the notion of category-based routing. The goal is to
assign a set of categories to each node of a graph such that greedy routing is
possible. By proving bounds on the number of categories a node has to be in we
can argue about the plausibility of the underlying sociological model. In this
paper we substantially improve the upper bounds introduced by Eppstein et al.
and prove new lower bounds.

Export

BibTeX

@online{Bringmann2012Remarks,
TITLE = {Remarks on Category-based Routing in Social Networks},
AUTHOR = {Bringmann, Karl and Mehlhorn, Kurt and Neumann, Adrian},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1202.2293},
EPRINT = {1202.2293},
EPRINTTYPE = {arXiv},
YEAR = {2012},
ABSTRACT = {It is well known that individuals can route messages on short paths through social networks, given only simple information about the target and using only local knowledge about the topology. Sociologists conjecture that people find routes greedily by passing the message to an acquaintance that has more in common with the target than themselves, e.g. if a dentist in Saarbr\"ucken wants to send a message to a specific lawyer in Munich, he may forward it to someone who is a lawyer and/or lives in Munich. Modelling this setting, Eppstein et al. introduced the notion of category-based routing. The goal is to assign a set of categories to each node of a graph such that greedy routing is possible. By proving bounds on the number of categories a node has to be in we can argue about the plausibility of the underlying sociological model. In this paper we substantially improve the upper bounds introduced by Eppstein et al. and prove new lower bounds.},
}

Endnote

%0 Report
%A Bringmann, Karl
%A Mehlhorn, Kurt
%A Neumann, Adrian
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Remarks on Category-based Routing in Social Networks :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0018-AB51-B
%U http://arxiv.org/abs/1202.2293
%D 2012
%X It is well known that individuals can route messages on short paths through
social networks, given only simple information about the target and using only
local knowledge about the topology. Sociologists conjecture that people find
routes greedily by passing the message to an acquaintance that has more in
common with the target than themselves, e.g. if a dentist in Saarbr\"ucken
wants to send a message to a specific lawyer in Munich, he may forward it to
someone who is a lawyer and/or lives in Munich. Modelling this setting,
Eppstein et al. introduced the notion of category-based routing. The goal is to
assign a set of categories to each node of a graph such that greedy routing is
possible. By proving bounds on the number of categories a node has to be in we
can argue about the plausibility of the underlying sociological model. In this
paper we substantially improve the upper bounds introduced by Eppstein et al.
and prove new lower bounds.
%K cs.SI,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Discrete Mathematics, cs.DM, Physics, Physics and Society, physics.soc-ph

[118]

K. Bringmann and K. Panagiotou, “Efficient Sampling Methods for Discrete Distributions,” in Automata, Languages, and Programming (ICALP 2012), Warwick, UK, 2012.

Abstract

We study the fundamental problem of the exact and efficient generation of
random values from a finite and discrete probability distribution. Suppose that
we are given n distinct events with associated probabilities p_1,...,p_n. We
consider the problem of sampling a subset, which includes the i-th event
independently with probability p_i, and the problem of sampling from the
distribution, where the i-th event has a probability proportional to p_i. For
both problems we present on two different classes of inputs � sorted and
general probabilities � efficient preprocessing algorithms that allow for
asymptotically optimal querying, and prove almost matching lower bounds for
their complexity.

Export

BibTeX

@inproceedings{BringmannP12,
TITLE = {Efficient Sampling Methods for Discrete Distributions},
AUTHOR = {Bringmann, Karl and Panagiotou, Konstantinos},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31593-0},
DOI = {10.1007/978-3-642-31594-7_12},
LOCALID = {Local-ID: 76C613922FECC644C1257AD300348137-BringmannP12},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
ABSTRACT = {We study the fundamental problem of the exact and efficient generation of random values from a finite and discrete probability distribution. Suppose that we are given n distinct events with associated probabilities p_1,...,p_n. We consider the problem of sampling a subset, which includes the i-th event independently with probability p_i, and the problem of sampling from the distribution, where the i-th event has a probability proportional to p_i. For both problems we present on two different classes of inputs {\diamond} sorted and general probabilities {\diamond} efficient preprocessing algorithms that allow for asymptotically optimal querying, and prove almost matching lower bounds for their complexity.},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew M. and Wattenhofer, Roger},
PAGES = {133--144},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7391},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%A Bringmann, Karl
%A Panagiotou, Konstantinos
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Efficient Sampling Methods for Discrete Distributions :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BBDB-2
%R 10.1007/978-3-642-31594-7_12
%F OTHER: Local-ID: 76C613922FECC644C1257AD300348137-BringmannP12
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%C Warwick, UK
%X We study the fundamental problem of the exact and efficient generation of
random values from a finite and discrete probability distribution. Suppose that
we are given n distinct events with associated probabilities p_1,...,p_n. We
consider the problem of sampling a subset, which includes the i-th event
independently with probability p_i, and the problem of sampling from the
distribution, where the i-th event has a probability proportional to p_i. For
both problems we present on two different classes of inputs � sorted and
general probabilities � efficient preprocessing algorithms that allow for
asymptotically optimal querying, and prove almost matching lower bounds for
their complexity.
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew M.; Wattenhofer, Roger
%P 133 - 144
%I Springer
%@ 978-3-642-31593-0
%B Lecture Notes in Computer Science
%N 7391
%@ false

[119]

M. Cygan, S. Kratsch, M. Pilipczuk, M. Pilipczuk, and M. Wahlström, “Clique Cover and Graph Separation: New Incompressibility Results,” in Automata, Languages, and Programming (ICALP 2012), Warwick, UK, 2012.

Export

BibTeX

@inproceedings{CyganKratschPilipczukPilipczukWahlstroem2012,
TITLE = {Clique Cover and Graph Separation: New Incompressibility Results},
AUTHOR = {Cygan, Marek and Kratsch, Stefan and Pilipczuk, Marcin and Pilipczuk, Micha and Wahlstr{\"o}m, Magnus},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31593-0},
DOI = {10.1007/978-3-642-31594-7_22},
LOCALID = {Local-ID: 5A998CDCF7D0A3FCC1257AD4004D05AF-CyganKratschPilipczukPilipczukWahlstroem2012},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew M. and Wattenhofer, Roger},
PAGES = {254--265},
SERIES = {Lecture Notes in Computer Science},
DEBUG = {author: Wattenhofer, Roger},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew},
VOLUME = {7391},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%A Cygan, Marek
%A Kratsch, Stefan
%A Pilipczuk, Marcin
%A Pilipczuk, Micha
%A Wahlström, Magnus
%+ External Organizations
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Clique Cover and Graph Separation: New Incompressibility Results :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BC4B-B
%R 10.1007/978-3-642-31594-7_22
%F OTHER: Local-ID: 5A998CDCF7D0A3FCC1257AD4004D05AF-CyganKratschPilipczukPilipczukWahlstroem2012
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%C Warwick, UK
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew M.; Wattenhofer, Roger
%P 254 - 265
%I Springer
%@ 978-3-642-31593-0
%B Lecture Notes in Computer Science
%Y Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew; Wattenhofer, Roger
%N 7391
%@ false

[120]

A. Czumaj, K. Mehlhorn, A. Pitts, and R. Wattenhofer, Eds., Automata, Languages, and Programming. Springer, 2012.

Export

BibTeX

@proceedings{KurtLNCS7392,
TITLE = {Automata, Languages, and Programming},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew and Wattenhofer, Roger},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31584-8},
DOI = {10.1007/978-3-642-31585-5},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7392},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%E Czumaj, Artur
%E Mehlhorn, Kurt
%E Pitts, Andrew
%E Wattenhofer, Roger
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Automata, Languages, and Programming : 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part II
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A441-A
%R 10.1007/978-3-642-31585-5
%@ 978-3-642-31584-8
%I Springer
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%D 2012
%C Warwick, UK
%S Lecture Notes in Computer Science
%V 7392
%@ false

[121]

A. Czumaj, K. Mehlhorn, A. Pitts, and R. Wattenhofer, Eds., Automata, Languages, and Programming. Springer, 2012.

Export

BibTeX

@proceedings{KurtLNCS7391,
TITLE = {Automata, Languages, and Programming},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew and Wattenhofer, Roger},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31593-0},
DOI = {10.1007/978-3-642-31594-7},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7391},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%E Czumaj, Artur
%E Mehlhorn, Kurt
%E Pitts, Andrew
%E Wattenhofer, Roger
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
%T Automata, Languages, and Programming : 39th International Colloquium, ICALP 2012, Warwick, UK, July 9-13, 2012, Proceedings, Part I
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A43E-3
%R 10.1007/978-3-642-31594-7
%@ 978-3-642-31593-0
%I Springer
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%D 2012
%C Warwick, UK
%S Lecture Notes in Computer Science
%V 7391
%@ false

[122]

K. Elbassioni, “A QPTAS for ε-Envy-free Profit-maximizing Pricing on Line Graphs,” in Automata, Languages, and Programming (ICALP 2012), Warwick, UK, 2012.

Export

BibTeX

@inproceedings{Elbassioni2012e,
TITLE = {A {QPTAS} for $\varepsilon$-Envy-free Profit-maximizing Pricing on Line Graphs},
AUTHOR = {Elbassioni, Khaled},
LANGUAGE = {eng},
ISBN = {978-3-642-31584-8; 978-3-642-31585-5},
DOI = {10.1007/978-3-642-31585-5_46},
LOCALID = {Local-ID: 140EF868CCF427F9C1257AD40047FB11-Elbassioni2012e},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew M. and Wattenhofer, Roger},
PAGES = {513--524},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7392},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%A Elbassioni, Khaled
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A QPTAS for ε-Envy-free Profit-maximizing Pricing on Line Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BC8C-A
%R 10.1007/978-3-642-31585-5_46
%F OTHER: Local-ID: 140EF868CCF427F9C1257AD40047FB11-Elbassioni2012e
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%C Warwick, UK
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew M.; Wattenhofer, Roger
%P 513 - 524
%I Springer
%@ 978-3-642-31584-8 978-3-642-31585-5
%B Lecture Notes in Computer Science
%N 7392

[123]

A. Elmasry, K. Mehlhorn, and J. M. Schmidt, “An O(n+ m) Certifying Triconnnectivity Algorithm for Hamiltonian Graphs,” Algorithmica, vol. 62, no. 3, 2012.

Export

BibTeX

@article{Elmasry2012,
TITLE = {An O(n+ m) Certifying Triconnnectivity Algorithm for {H}amiltonian Graphs},
AUTHOR = {Elmasry, Amr and Mehlhorn, Kurt and Schmidt, Jens M.},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-010-9481-2},
LOCALID = {Local-ID: C1256428004B93B8-A45F18DF4E1C7C57C1257846003F6ADF-ElmasryMehlhornSchmidt2010},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2012},
DATE = {2012},
JOURNAL = {Algorithmica},
VOLUME = {62},
NUMBER = {3},
PAGES = {754--766},
}

Endnote

%0 Journal Article
%A Elmasry, Amr
%A Mehlhorn, Kurt
%A Schmidt, Jens M.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T An O(n+ m) Certifying Triconnnectivity Algorithm for Hamiltonian Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-15F9-4
%F EDOC: 536712
%R 10.1007/s00453-010-9481-2
%F OTHER: Local-ID: C1256428004B93B8-A45F18DF4E1C7C57C1257846003F6ADF-ElmasryMehlhornSchmidt2010
%7 2010
%D 2012
%J Algorithmica
%V 62
%N 3
%& 754
%P 754 - 766
%I Springer
%C New York, NY
%@ false

[124]

T. Jurkiewicz and K. Mehlhorn, “The Cost of Address Translation,” 2012. [Online]. Available: http://arxiv.org/abs/1212.0703. (arXiv: 1212.0703)

Abstract

Modern computers are not random access machines (RAMs). They have a memory
hierarchy, multiple cores, and virtual memory. In this paper, we address the
computational cost of address translation in virtual memory. Starting point for
our work is the observation that the analysis of some simple algorithms (random
scan of an array, binary search, heapsort) in either the RAM model or the EM
model (external memory model) does not correctly predict growth rates of actual
running times. We propose the VAT model (virtual address translation) to
account for the cost of address translations and analyze the algorithms
mentioned above and others in the model. The predictions agree with the
measurements. We also analyze the VAT-cost of cache-oblivious algorithms.

Export

BibTeX

@online{Jurkiewicz2012,
TITLE = {The Cost of Address Translation},
AUTHOR = {Jurkiewicz, Tomasz and Mehlhorn, Kurt},
LANGUAGE = {eng},
URL = {http://arxiv.org/abs/1212.0703},
EPRINT = {1212.0703},
EPRINTTYPE = {arXiv},
YEAR = {2012},
ABSTRACT = {Modern computers are not random access machines (RAMs). They have a memory hierarchy, multiple cores, and virtual memory. In this paper, we address the computational cost of address translation in virtual memory. Starting point for our work is the observation that the analysis of some simple algorithms (random scan of an array, binary search, heapsort) in either the RAM model or the EM model (external memory model) does not correctly predict growth rates of actual running times. We propose the VAT model (virtual address translation) to account for the cost of address translations and analyze the algorithms mentioned above and others in the model. The predictions agree with the measurements. We also analyze the VAT-cost of cache-oblivious algorithms.},
}

Endnote

%0 Report
%A Jurkiewicz, Tomasz
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Cost of Address Translation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0015-8653-C
%U http://arxiv.org/abs/1212.0703
%D 2012
%X Modern computers are not random access machines (RAMs). They have a memory
hierarchy, multiple cores, and virtual memory. In this paper, we address the
computational cost of address translation in virtual memory. Starting point for
our work is the observation that the analysis of some simple algorithms (random
scan of an array, binary search, heapsort) in either the RAM model or the EM
model (external memory model) does not correctly predict growth rates of actual
running times. We propose the VAT model (virtual address translation) to
account for the cost of address translations and analyze the algorithms
mentioned above and others in the model. The predictions agree with the
measurements. We also analyze the VAT-cost of cache-oblivious algorithms.
%K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,Computer Science, Performance, cs.PF,

[125]

D. Kane, K. Mehlhorn, T. Sauerwald, and H. Sun, “Counting Arbitrary Subgraphs in Data Streams,” in Automata, Languages, and Programming (ICALP 2012), Warwick, UK, 2012.

Export

BibTeX

@inproceedings{Sun2012b,
TITLE = {Counting Arbitrary Subgraphs in Data Streams},
AUTHOR = {Kane, Daniel and Mehlhorn, Kurt and Sauerwald, Thomas and Sun, He},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31584-8},
DOI = {10.1007/978-3-642-31585-5},
LOCALID = {Local-ID: D59F81728CEDD0B9C1257AD000568326-Sun2012b},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew M. and Wattenhofer, Roger},
PAGES = {598--609},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7392},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%A Kane, Daniel
%A Mehlhorn, Kurt
%A Sauerwald, Thomas
%A Sun, He
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Counting Arbitrary Subgraphs in Data Streams :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BDD7-D
%R 10.1007/978-3-642-31585-5
%F OTHER: Local-ID: D59F81728CEDD0B9C1257AD000568326-Sun2012b
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%C Warwick, UK
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew M.; Wattenhofer, Roger
%P 598 - 609
%I Springer
%@ 978-3-642-31584-8
%B Lecture Notes in Computer Science
%N 7392
%@ false

[126]

S. Kratsch, M. Pilipczuk, M. Pilipczuk, and M. Wahlström, “Fixed-parameter Tractability of Multicut in Directed Acyclic Graphs,” in Automata, Languages, and Programming (ICALP 2012), Warwick, UK, 2012.

Export

BibTeX

@inproceedings{KratschPilipczukPilipczukWahlstroem2012,
TITLE = {Fixed-parameter Tractability of Multicut in Directed Acyclic Graphs},
AUTHOR = {Kratsch, Stefan and Pilipczuk, Marcin and Pilipczuk, Micha and Wahlstr{\"o}m, Magnus},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31593-0},
DOI = {10.1007/978-3-642-31594-7_49},
LOCALID = {Local-ID: E10E3826E7217AEBC1257AD4004D690C-KratschPilipczukPilipczukWahlstroem2012},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew M. and Wattenhofer, Roger},
PAGES = {581--593},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7391},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%A Kratsch, Stefan
%A Pilipczuk, Marcin
%A Pilipczuk, Micha
%A Wahlström, Magnus
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Fixed-parameter Tractability of Multicut in Directed Acyclic Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BE86-C
%R 10.1007/978-3-642-31594-7_49
%F OTHER: Local-ID: E10E3826E7217AEBC1257AD4004D690C-KratschPilipczukPilipczukWahlstroem2012
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%C Warwick, UK
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew M.; Wattenhofer, Roger
%P 581 - 593
%I Springer
%@ 978-3-642-31593-0
%B Lecture Notes in Computer Science
%N 7391
%@ false

[127]

N. Megow, K. Mehlhorn, and P. Schweitzer, “Online Graph Exploration: New Results on Old and New Algorithms,” Theoretical Computer Science, vol. 463, 2012.

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BibTeX

@article{MegowMehlhornSchweitzer2012,
TITLE = {Online Graph Exploration: New Results on Old and New Algorithms},
AUTHOR = {Megow, Nicole and Mehlhorn, Kurt and Schweitzer, Pascal},
LANGUAGE = {eng},
ISSN = {0304-3975},
DOI = {10.1016/j.tcs.2012.06.034},
LOCALID = {Local-ID: 18D093BE87A59A63C1257AC5007EF50F-MegowMehlhornSchweitzer2012},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2012},
DATE = {2012},
JOURNAL = {Theoretical Computer Science},
VOLUME = {463},
PAGES = {62--72},
}

Endnote

%0 Journal Article
%A Megow, Nicole
%A Mehlhorn, Kurt
%A Schweitzer, Pascal
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Online Graph Exploration: New Results on Old and New Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-C49C-7
%R 10.1016/j.tcs.2012.06.034
%F OTHER: Local-ID: 18D093BE87A59A63C1257AC5007EF50F-MegowMehlhornSchweitzer2012
%7 2012-07-08
%D 2012
%J Theoretical Computer Science
%V 463
%& 62
%P 62 - 72
%I Elsevier
%C Amsterdam
%@ false

[128]

N. Megow, M. Skutella, J. Verschae, and A. Wiese, “The Power of Recourse for Online MST and TSP,” in Automata, Languages, and Programming (ICALP 2012), Warwick, 2012.

Export

BibTeX

@inproceedings{MegowSVW2012,
TITLE = {The Power of Recourse for Online {MST} and {TSP}},
AUTHOR = {Megow, Nicole and Skutella, Martin and Verschae, Jose and Wiese, Andreas},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31593-0},
DOI = {10.1007/978-3-642-31594-7_58},
LOCALID = {Local-ID: F9D0FE85F8D1AF2FC1257AC5007D0CF8-MegowSVW2012},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew M. and Wattenhofer, Roger},
PAGES = {689--700},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7391},
ADDRESS = {Warwick},
}

Endnote

%0 Conference Proceedings
%A Megow, Nicole
%A Skutella, Martin
%A Verschae, Jose
%A Wiese, Andreas
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Power of Recourse for Online MST and TSP :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BE8E-B
%R 10.1007/978-3-642-31594-7_58
%F OTHER: Local-ID: F9D0FE85F8D1AF2FC1257AC5007D0CF8-MegowSVW2012
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-11-29 - 2012-11-29
%C Warwick
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew M.; Wattenhofer, Roger
%P 689 - 700
%I Springer
%@ 978-3-642-31593-0
%B Lecture Notes in Computer Science
%N 7391
%@ false

[129]

K. Mehlhorn and J.-R. Sack, “CGTA-Awards 2011,” Computational Geometry: Theory and Applications, vol. 45, no. 4, 2012.

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BibTeX

@article{Mehlhorn2012139,
TITLE = {{CGTA}-Awards 2011},
AUTHOR = {Mehlhorn, Kurt and Sack, Joerg-Ruediger},
LANGUAGE = {eng},
ISSN = {0925-7721},
DOI = {10.1016/j.comgeo.2011.11.005},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2012},
DATE = {2012},
JOURNAL = {Computational Geometry: Theory and Applications},
VOLUME = {45},
NUMBER = {4},
PAGES = {139--139},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Sack, Joerg-Ruediger
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T CGTA-Awards 2011 :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-5E87-4
%R 10.1016/j.comgeo.2011.11.005
%7 2012
%D 2012
%J Computational Geometry: Theory and Applications
%V 45
%N 4
%& 139
%P 139 - 139
%I Elsevier
%C Amsterdam
%@ false

[130]

J. M. Schmidt, “Certifying 3-Connectivity in Linear Time,” in Automata, Languages, and Programming (ICALP 2012), Warwick, UK, 2012.

Export

BibTeX

@inproceedings{Schmidt2012b,
TITLE = {Certifying 3-Connectivity in Linear Time},
AUTHOR = {Schmidt, Jens M.},
LANGUAGE = {eng},
ISSN = {0302-9743},
ISBN = {978-3-642-31593-0},
DOI = {10.1007/978-3-642-31594-7_66},
LOCALID = {Local-ID: 9F99A9B8CE9D07A0C1257AC2004AE457-Schmidt2012b},
PUBLISHER = {Springer},
YEAR = {2012},
DATE = {2012},
BOOKTITLE = {Automata, Languages, and Programming (ICALP 2012)},
EDITOR = {Czumaj, Artur and Mehlhorn, Kurt and Pitts, Andrew and Wattenhofer, Roger},
PAGES = {786--797},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {7391},
ADDRESS = {Warwick, UK},
}

Endnote

%0 Conference Proceedings
%A Schmidt, Jens M.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying 3-Connectivity in Linear Time :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-BEEC-6
%R 10.1007/978-3-642-31594-7_66
%F OTHER: Local-ID: 9F99A9B8CE9D07A0C1257AC2004AE457-Schmidt2012b
%D 2012
%B 39th International Colloquium on Automata, Languages, and Programming
%Z date of event: 2012-07-09 - 2012-07-13
%C Warwick, UK
%B Automata, Languages, and Programming
%E Czumaj, Artur; Mehlhorn, Kurt; Pitts, Andrew; Wattenhofer, Roger
%P 786 - 797
%I Springer
%@ 978-3-642-31593-0
%B Lecture Notes in Computer Science
%N 7391
%@ false

2011

[131]

E. Alkassar, S. Böhme, K. Mehlhorn, and C. Rizkallah, “Verification of Certifying Computations,” in Computer Aided Verification, Snowbird, Utah, USA, 2011.

Abstract

Formal verification of complex algorithms is challenging. Verifying their
implementations goes beyond the state of the art of
current verification tools and proving their correctness usually
involves non-trivial mathematical theorems.
Certifying algorithms compute in addition to each output a
witness certifying that the output is correct. A checker for such a witness
is usually much simpler than the original algorithm -- yet it is all the
user has to trust. Verification of checkers is feasible with current tools and
leads to computations that can be completely trusted.
In this paper we develop a framework to seamlessly verify certifying
computations. The automatic verifier VCC is used for checking code
correctness, and the interactive theorem prover Isabelle/HOL targets
high-level mathematical properties of algorithms. We demonstrate the
effectiveness of our approach by applying it to the verification of
the algorithmic library LEDA.

Export

BibTeX

@inproceedings{FormalVerificationofCertifyingComputations,
TITLE = {Verification of Certifying Computations},
AUTHOR = {Alkassar, Eyad and B{\"o}hme, Sascha and Mehlhorn, Kurt and Rizkallah, Christine},
LANGUAGE = {eng},
ISBN = {978-3-642-22109-5},
URL = {http://www.mpi-inf.mpg.de/~mehlhorn/ftp/VerificationCertComps.pdf},
DOI = {10.1007/978-3-642-22110-1_7},
LOCALID = {Local-ID: C1256428004B93B8-5C01AA7BBEAB7C26C125785C003095BF-FormalVerificationofCertifyingComputations},
PUBLISHER = {Springer},
YEAR = {2011},
DATE = {2011},
ABSTRACT = {Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current verification tools and proving their correctness usually involves non-trivial mathematical theorems. Certifying algorithms compute in addition to each output a witness certifying that the output is correct. A checker for such a witness is usually much simpler than the original algorithm -- yet it is all the user has to trust. Verification of checkers is feasible with current tools and leads to computations that can be completely trusted. In this paper we develop a framework to seamlessly verify certifying computations. The automatic verifier VCC is used for checking code correctness, and the interactive theorem prover Isabelle/HOL targets high-level mathematical properties of algorithms. We demonstrate the effectiveness of our approach by applying it to the verification of the algorithmic library LEDA.},
BOOKTITLE = {Computer Aided Verification},
EDITOR = {Gopalakrishnan, Ganesh and Qadeer, Shaz},
PAGES = {67--82},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {6806},
ADDRESS = {Snowbird, Utah, USA},
}

Endnote

%0 Conference Proceedings
%A Alkassar, Eyad
%A Böhme, Sascha
%A Mehlhorn, Kurt
%A Rizkallah, Christine
%+ Cluster of Excellence Multimodal Computing and Interaction
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Verification of Certifying Computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-12BF-E
%F EDOC: 618673
%R 10.1007/978-3-642-22110-1_7
%U http://www.mpi-inf.mpg.de/~mehlhorn/ftp/VerificationCertComps.pdf
%F OTHER: Local-ID: C1256428004B93B8-5C01AA7BBEAB7C26C125785C003095BF-FormalVerificationofCertifyingComputations
%D 2011
%B CAV 2011
%Z date of event: 2011-07-14 - 2011-07-20
%C Snowbird, Utah, USA
%X Formal verification of complex algorithms is challenging. Verifying their
implementations goes beyond the state of the art of
current verification tools and proving their correctness usually
involves non-trivial mathematical theorems.
Certifying algorithms compute in addition to each output a
witness certifying that the output is correct. A checker for such a witness
is usually much simpler than the original algorithm -- yet it is all the
user has to trust. Verification of checkers is feasible with current tools and
leads to computations that can be completely trusted.
In this paper we develop a framework to seamlessly verify certifying
computations. The automatic verifier VCC is used for checking code
correctness, and the interactive theorem prover Isabelle/HOL targets
high-level mathematical properties of algorithms. We demonstrate the
effectiveness of our approach by applying it to the verification of
the algorithmic library LEDA.
%B Computer Aided Verification
%E Gopalakrishnan, Ganesh; Qadeer, Shaz
%P 67 - 82
%I Springer
%@ 978-3-642-22109-5
%B Lecture Notes in Computer Science
%N 6806

[132]

E. Alkassar, S. Böhme, K. Mehlhorn, C. Rizkallah, and P. Schweitzer, “An Introduction to Certifying Algorithms,” Information technology, vol. 53, no. 6, 2011.

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BibTeX

@article{Mehlhornit2011,
TITLE = {An Introduction to Certifying Algorithms},
AUTHOR = {Alkassar, Eyad and B{\"o}hme, Sascha and Mehlhorn, Kurt and Rizkallah, Christine and Schweitzer, Pascal},
LANGUAGE = {eng},
ISSN = {1611-2776},
PUBLISHER = {Oldenbourg Wissenschaftsverlag},
ADDRESS = {M{\"u}nchen},
YEAR = {2011},
JOURNAL = {Information technology},
VOLUME = {53},
NUMBER = {6},
PAGES = {287--293},
}

Endnote

%0 Journal Article
%A Alkassar, Eyad
%A Böhme, Sascha
%A Mehlhorn, Kurt
%A Rizkallah, Christine
%A Schweitzer, Pascal
%+ International Max Planck Research School, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T An Introduction to Certifying Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A46F-6
%7 2011
%D 2011
%J Information technology
%O it
%V 53
%N 6
%& 287
%P 287 - 293
%I Oldenbourg Wissenschaftsverlag
%C München
%@ false

[133]

E. Amaldi, C. Iuliano, T. Jurkiewicz, K. Mehlhorn, and R. Rizzi, “Improved Minimum Cycle Bases Algorithms by Restriction to Isometric Cycles.” 2011.

Export

BibTeX

@misc{Amaldi2011,
TITLE = {Improved Minimum Cycle Bases Algorithms by Restriction to Isometric Cycles},
AUTHOR = {Amaldi, Edoardo and Iuliano, Claudio and Jurkiewicz, Tomasz and Mehlhorn, Kurt and Rizzi, Romeo},
LANGUAGE = {eng},
YEAR = {2011},
}

Endnote

%0 Report
%A Amaldi, Edoardo
%A Iuliano, Claudio
%A Jurkiewicz, Tomasz
%A Mehlhorn, Kurt
%A Rizzi, Romeo
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Improved Minimum Cycle Bases Algorithms by Restriction to
Isometric Cycles :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002B-4C4C-D
%D 2011

[134]

S. Baswana, T. Kavitha, K. Mehlhorn, and S. Pettie, “Additive Spanners and (α, β)-Spanners,” ACM Transactions on Algorithms, vol. 7, no. 1, 2011.

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BibTeX

@article{MehlhornTALG2011,
TITLE = {Additive Spanners and ($\alpha$, $\beta$)-Spanners},
AUTHOR = {Baswana, Surender and Kavitha, Telikepalli and Mehlhorn, Kurt and Pettie, Seth},
LANGUAGE = {eng},
ISSN = {1549-6325},
URL = {http://doi.acm.org/10.1145/1868237.1868242},
DOI = {10.1145/1868237.1868242},
LOCALID = {Local-ID: C1256428004B93B8-150FC93C5EEE2627C12579C90051FFA8-MehlhornTALG2011},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2011},
DATE = {2011},
JOURNAL = {ACM Transactions on Algorithms},
VOLUME = {7},
NUMBER = {1},
PAGES = {5:1--5:26},
EID = {5},
}

Endnote

%0 Journal Article
%A Baswana, Surender
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Pettie, Seth
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Additive Spanners and (α, β)-Spanners :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-11D8-B
%F EDOC: 618744
%R 10.1145/1868237.1868242
%U http://doi.acm.org/10.1145/1868237.1868242
%F OTHER: Local-ID: C1256428004B93B8-150FC93C5EEE2627C12579C90051FFA8-MehlhornTALG2011
%7 2011
%D 2011
%* Review method: peer-reviewed
%J ACM Transactions on Algorithms
%V 7
%N 1
%& 5:1
%P 5:1 - 5:26
%Z sequence number: 5
%I ACM
%C New York, NY
%@ false

[135]

G. Christodoulou, K. Mehlhorn, and E. Pyrga, “Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms,” in Algorithms - ESA 2011, Saarbrücken, Germany, 2011.

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BibTeX

@inproceedings{Becker2011,
TITLE = {Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms},
AUTHOR = {Christodoulou, George and Mehlhorn, Kurt and Pyrga, Evangelia},
LANGUAGE = {eng},
ISBN = {978-3-642-23718-8},
URL = {http://dx.doi.org/10.1007/978-3-642-23719-5_11},
DOI = {10.1007/978-3-642-23719-5_11},
LOCALID = {Local-ID: C1256428004B93B8-D203A9C35EF58BBAC12579A3004010FD-Becker2011},
PUBLISHER = {Springer},
YEAR = {2011},
DATE = {2011},
BOOKTITLE = {Algorithms -- ESA 2011},
EDITOR = {Demetrescu, Camil and Halld{\'o}rsson, Mang{\'u}s M.},
PAGES = {119--130},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {6942},
ADDRESS = {Saarbr{\"u}cken, Germany},
}

Endnote

%0 Conference Proceedings
%A Christodoulou, George
%A Mehlhorn, Kurt
%A Pyrga, Evangelia
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-1240-6
%F EDOC: 618742
%R 10.1007/978-3-642-23719-5_11
%U http://dx.doi.org/10.1007/978-3-642-23719-5_11
%F OTHER: Local-ID: C1256428004B93B8-D203A9C35EF58BBAC12579A3004010FD-Becker2011
%D 2011
%B 19th Annual European Symposium on
%Z date of event: 2011-09-05 - 2011-09-09
%C Saarbrücken, Germany
%B Algorithms - ESA 2011
%E Demetrescu, Camil; Halldórsson, Mangús M.
%P 119 - 130
%I Springer
%@ 978-3-642-23718-8
%B Lecture Notes in Computer Science
%N 6942

[136]

A. Eigenwillig and K. Mehlhorn, “Multiplication of Long Integers -- Faster than Long Multiplication,” in Algorithms Unplugged, Berlin: Springer, 2011.

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BibTeX

@incollection{EigenwilligMehlhorn2011,
TITLE = {Multiplication of Long Integers -- Faster than Long Multiplication},
AUTHOR = {Eigenwillig, Arno and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-642-15327-3},
DOI = {10.1007/978-3-642-15328-0_11},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2011},
DATE = {2011},
BOOKTITLE = {Algorithms Unplugged},
EDITOR = {V{\"o}cking, Berthold and Alt, Helmut and Dietzfelbinger, Martin and Reischuk, R{\"u}diger and Scheideler, Christian and Vollmer, Heribert and Wagner, Dorothea},
PAGES = {101--109},
}

Endnote

%0 Book Section
%A Eigenwillig, Arno
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Multiplication of Long Integers -- Faster than Long Multiplication :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002B-4C8F-8
%R 10.1007/978-3-642-15328-0_11
%D 2011
%B Algorithms Unplugged
%E Vöcking, Berthold; Alt, Helmut; Dietzfelbinger, Martin; Reischuk, Rüdiger; Scheideler, Christian; Vollmer, Heribert; Wagner, Dorothea
%P 101 - 109
%I Springer
%C Berlin
%@ 978-3-642-15327-3

[137]

D. Halperin and K. Mehlhorn, “Guest Editorial: Selected Papers from European Symposium on Algorithms,” Algorithmica, vol. 60, no. 1, 2011.

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BibTeX

@article{KurtAlg60,
TITLE = {Guest Editorial: Selected Papers from European Symposium on Algorithms},
AUTHOR = {Halperin, Dan and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0178-4617},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2011},
DATE = {2011},
JOURNAL = {Algorithmica},
VOLUME = {60},
NUMBER = {1},
PAGES = {1--2},
}

Endnote

%0 Journal Article
%A Halperin, Dan
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Guest Editorial: Selected Papers from European Symposium on Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0024-A469-1
%7 2011
%D 2011
%J Algorithmica
%V 60
%N 1
%& 1
%P 1 - 2
%I Springer
%C New York, NY
%@ false

[138]

T. Kavitha, K. Mehlhorn, and D. Michail, “New Approximation Algorithms for Minimum Cycle Bases of Graphs,” Algorithmica, vol. 59, no. 4, 2011.

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BibTeX

@article{KavithaALG2011,
TITLE = {New Approximation Algorithms for Minimum Cycle Bases of Graphs},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
ISSN = {0178-4617},
URL = {http://dx.doi.org/10.1007/s00453-009-9313-4},
DOI = {10.1007/s00453-009-9313-4},
LOCALID = {Local-ID: C1256428004B93B8-9DF47B615A95B3B9C12579CA0043E5C0-KavithaALG2011},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2011},
DATE = {2011},
JOURNAL = {Algorithmica},
VOLUME = {59},
NUMBER = {4},
PAGES = {471--488},
}

Endnote

%0 Journal Article
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New Approximation Algorithms for Minimum Cycle Bases of Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-125C-A
%F EDOC: 618754
%R 10.1007/s00453-009-9313-4
%U http://dx.doi.org/10.1007/s00453-009-9313-4
%F OTHER: Local-ID: C1256428004B93B8-9DF47B615A95B3B9C12579CA0043E5C0-KavithaALG2011
%D 2011
%* Review method: peer-reviewed
%J Algorithmica
%V 59
%N 4
%& 471
%P 471 - 488
%I Springer
%C New York, NY
%@ false

[139]

M. Manjunath, K. Mehlhorn, K. Panagiotou, and H. Sun, “Approximate Counting of Cycles in Streams,” in Algorithms – ESA 2011, 2011.

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BibTeX

@inproceedings{Sun2011z,
TITLE = {Approximate Counting of Cycles in Streams},
AUTHOR = {Manjunath, Madhusudan and Mehlhorn, Kurt and Panagiotou, Konstantinos and Sun, He},
LANGUAGE = {eng},
DOI = {10.1007/978-3-642-23719-5_57},
PUBLISHER = {Springer},
YEAR = {2011},
DATE = {2011},
BOOKTITLE = {Algorithms -- ESA 2011},
EDITOR = {Demetrescu, Camil and M. Halld{\'o}rsson, Magn{\'u}s},
PAGES = {677--688},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {6942},
}

Endnote

%0 Conference Proceedings
%A Manjunath, Madhusudan
%A Mehlhorn, Kurt
%A Panagiotou, Konstantinos
%A Sun, He
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Approximate Counting of Cycles in Streams :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-85DB-D
%R 10.1007/978-3-642-23719-5_57
%D 2011
%B ESA 2011
%Z date of event: -
%B Algorithms – ESA 2011
%E Demetrescu, Camil; M. Halldórsson, Magnús
%P 677 - 688
%I Springer
%B Lecture Notes in Computer Science
%N 6942

[140]

N. Megow, K. Mehlhorn, and P. Schweitzer, “Online Graph Exploration: New Results on Old and New Algorithms,” in Automata, Languages and Programming (ICALP 2011), Zurich, Switzerland, 2011.

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BibTeX

@inproceedings{Megow2011-explore,
TITLE = {Online Graph Exploration: New Results on Old and New Algorithms},
AUTHOR = {Megow, Nicole and Mehlhorn, Kurt and Schweitzer, Pascal},
LANGUAGE = {eng},
ISBN = {978-3-642-22011-1},
URL = {http://dx.doi.org/10.1007/978-3-642-22012-8_38},
DOI = {10.1007/978-3-642-22012-8_38},
LOCALID = {Local-ID: C1256428004B93B8-19606035D4D26455C12578810025513C-Megow2011-explore},
PUBLISHER = {Springer},
YEAR = {2011},
DATE = {2011},
BOOKTITLE = {Automata, Languages and Programming (ICALP 2011)},
EDITOR = {Aceto, Luca and Henzinger, Monika and Sgall, Ji{\v r}{\'i}},
PAGES = {478--489},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {6756},
ADDRESS = {Zurich, Switzerland},
}

Endnote

%0 Conference Proceedings
%A Megow, Nicole
%A Mehlhorn, Kurt
%A Schweitzer, Pascal
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Online Graph Exploration: New Results on Old and New Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-1266-3
%F EDOC: 618681
%R 10.1007/978-3-642-22012-8_38
%U http://dx.doi.org/10.1007/978-3-642-22012-8_38
%F OTHER: Local-ID: C1256428004B93B8-19606035D4D26455C12578810025513C-Megow2011-explore
%D 2011
%B 38th International Colloquium on Automata, Languages and Programming
%Z date of event: 2011-07-04 - 2011-07-08
%C Zurich, Switzerland
%B Automata, Languages and Programming
%E Aceto, Luca; Henzinger, Monika; Sgall, Jiří
%P 478 - 489
%I Springer
%@ 978-3-642-22011-1
%B Lecture Notes in Computer Science
%N 6756

[141]

K. Mehlhorn and M. Sagraloff, “A Deterministic Algorithm for Isolating Real Roots of a Real Polynomial,” Journal of Symbolic Computation, vol. 46, no. 1, 2011.

Abstract

We describe a bisection algorithm for root isolation of polynomials with real
coefficients. It is assumed that the coefficients can be approximated with
arbitrary precision; exact computation in the field of coefficients is not
required. We refer to such coefficients as bitstream coefficients. The
algorithm is simpler, deterministic and has better asymptotic complexity than
the randomized algorithm of Eigenwillig et al. (2005). We also discuss a
partial extension to multiple roots.

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BibTeX

@article{MS:Bistream:2011,
TITLE = {A Deterministic Algorithm for Isolating Real Roots of a Real Polynomial},
AUTHOR = {Mehlhorn, Kurt and Sagraloff, Michael},
LANGUAGE = {eng},
URL = {http://dx.doi.org/10.1016/j.jsc.2010.09.004},
DOI = {10.1016/j.jsc.2010.09.004},
LOCALID = {Local-ID: C1256428004B93B8-A0FD28893140854AC125781C003E51F3-MS:Bistream:2011},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2011},
DATE = {2011},
ABSTRACT = {We describe a bisection algorithm for root isolation of polynomials with real coefficients. It is assumed that the coefficients can be approximated with arbitrary precision; exact computation in the field of coefficients is not required. We refer to such coefficients as bitstream coefficients. The algorithm is simpler, deterministic and has better asymptotic complexity than the randomized algorithm of Eigenwillig et al. (2005). We also discuss a partial extension to multiple roots.},
JOURNAL = {Journal of Symbolic Computation},
VOLUME = {46},
NUMBER = {1},
PAGES = {70--90},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Sagraloff, Michael
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Deterministic Algorithm for Isolating Real Roots of a Real Polynomial :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-11DA-7
%F EDOC: 618656
%R 10.1016/j.jsc.2010.09.004
%U http://dx.doi.org/10.1016/j.jsc.2010.09.004
%F OTHER: Local-ID: C1256428004B93B8-A0FD28893140854AC125781C003E51F3-MS:Bistream:2011
%7 2011
%D 2011
%* Review method: peer-reviewed
%X We describe a bisection algorithm for root isolation of polynomials with real
coefficients. It is assumed that the coefficients can be approximated with
arbitrary precision; exact computation in the field of coefficients is not
required. We refer to such coefficients as bitstream coefficients. The
algorithm is simpler, deterministic and has better asymptotic complexity than
the randomized algorithm of Eigenwillig et al. (2005). We also discuss a
partial extension to multiple roots.
%J Journal of Symbolic Computation
%V 46
%N 1
%& 70
%P 70 - 90
%I Elsevier
%C Amsterdam

[142]

K. Mehlhorn, R. Osbild, and M. Sagraloff, “A General Approach to the Analysis of Controlled Perturbation Algorithms,” Computational Geometry, vol. 44, no. 9, 2011.

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BibTeX

@article{MOS-CP2011,
TITLE = {A General Approach to the Analysis of Controlled Perturbation Algorithms},
AUTHOR = {Mehlhorn, Kurt and Osbild, Ralf and Sagraloff, Michael},
LANGUAGE = {eng},
URL = {http://dx.doi.org/10.1016/j.comgeo.2011.06.001},
DOI = {10.1016/j.comgeo.2011.06.001},
LOCALID = {Local-ID: C1256428004B93B8-2A5C0FDF3B7C1B18C1257861003B9A82-MOS-CP2011},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2011},
DATE = {2011},
JOURNAL = {Computational Geometry},
VOLUME = {44},
NUMBER = {9},
PAGES = {507--528},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Osbild, Ralf
%A Sagraloff, Michael
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A General Approach to the Analysis of Controlled Perturbation Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-11DC-3
%F EDOC: 618677
%R 10.1016/j.comgeo.2011.06.001
%U http://dx.doi.org/10.1016/j.comgeo.2011.06.001
%F OTHER: Local-ID: C1256428004B93B8-2A5C0FDF3B7C1B18C1257861003B9A82-MOS-CP2011
%7 2011
%D 2011
%* Review method: peer-reviewed
%J Computational Geometry
%V 44
%N 9
%& 507
%P 507 - 528
%I Elsevier
%C Amsterdam

[143]

N. Shervashidze, P. Schweitzer, E. J. van Leeuwen, K. Mehlhorn, and K. M. Borgwardt, “Weisfeiler-Lehman Graph Kernels,” Journal of Machine Learning Research, vol. 12, 2011.

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BibTeX

@article{Shervashidze2011,
TITLE = {{Weisfeiler}--{Lehman} Graph Kernels},
AUTHOR = {Shervashidze, Nino and Schweitzer, Pascal and van Leeuwen, Erik Jan and Mehlhorn, Kurt and Borgwardt, Karsten M.},
LANGUAGE = {eng},
ISSN = {1532-4435},
LOCALID = {Local-ID: C1256428004B93B8-11F8B9324866AC60C12579CA004E38AC-Shervashidze2011},
PUBLISHER = {MIT Press},
ADDRESS = {Cambridge, Mass.},
YEAR = {2011},
DATE = {2011},
JOURNAL = {Journal of Machine Learning Research},
VOLUME = {12},
PAGES = {2539--2561},
}

Endnote

%0 Journal Article
%A Shervashidze, Nino
%A Schweitzer, Pascal
%A van Leeuwen, Erik Jan
%A Mehlhorn, Kurt
%A Borgwardt, Karsten M.
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Weisfeiler-Lehman Graph Kernels :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0010-12C2-4
%F EDOC: 618759
%F OTHER: Local-ID: C1256428004B93B8-11F8B9324866AC60C12579CA004E38AC-Shervashidze2011
%7 2011
%D 2011
%* Review method: peer-reviewed
%J Journal of Machine Learning Research
%V 12
%& 2539
%P 2539 - 2561
%I MIT Press
%C Cambridge, Mass.
%@ false

2010

[144]

E. Berberich, E. Fogel, D. Halperin, K. Mehlhorn, and R. Wein, “Arrangements on Parametric Surfaces I: General Framework and Infrastructure,” Mathematics in Computer Science, vol. 4, no. 1, 2010.

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BibTeX

@article{bfhmw-aos1-2010,
TITLE = {Arrangements on Parametric Surfaces I: General Framework and Infrastructure},
AUTHOR = {Berberich, Eric and Fogel, Efi and Halperin, Dan and Mehlhorn, Kurt and Wein, Ron},
LANGUAGE = {eng},
ISSN = {1661-8270},
URL = {http://www.springerlink.com/content/gg0px81230557612/},
DOI = {10.1007/s11786-010-0042-5},
LOCALID = {Local-ID: C1256428004B93B8-745F1A8BE751371AC12577FB002DE576-bfhmw-aos1-2010},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2010},
DATE = {2010},
JOURNAL = {Mathematics in Computer Science},
VOLUME = {4},
NUMBER = {1},
PAGES = {45--66},
}

Endnote

%0 Journal Article
%A Berberich, Eric
%A Fogel, Efi
%A Halperin, Dan
%A Mehlhorn, Kurt
%A Wein, Ron
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Arrangements on Parametric Surfaces I: General Framework and Infrastructure :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-160D-0
%F EDOC: 536751
%R 10.1007/s11786-010-0042-5
%U http://www.springerlink.com/content/gg0px81230557612/
%F OTHER: Local-ID: C1256428004B93B8-745F1A8BE751371AC12577FB002DE576-bfhmw-aos1-2010
%D 2010
%* Review method: peer-reviewed
%J Mathematics in Computer Science
%V 4
%N 1
%& 45
%P 45 - 66
%I Springer
%C Berlin
%@ false

[145]

N. Garg, T. Kavitha, A. Kumar, K. Mehlhorn, and J. Mestre, “Assigning Papers to Referees,” Algorithmica, vol. 58, no. 1, 2010.

Export

BibTeX

@article{MehlhonMestre2009,
TITLE = {Assigning Papers to Referees},
AUTHOR = {Garg, Naveen and Kavitha, T. and Kumar, Amit and Mehlhorn, Kurt and Mestre, Juli{\'a}n},
LANGUAGE = {eng},
ISSN = {0178-4617},
URL = {http://dx.doi.org/10.1007/s00453-009-9386-0},
DOI = {10.1007/s00453-009-9386-0},
LOCALID = {Local-ID: C1256428004B93B8-213E0759D254F459C12576C500583EE4-MehlhonMestre2009},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2010},
DATE = {2010},
JOURNAL = {Algorithmica},
VOLUME = {58},
NUMBER = {1},
PAGES = {119--136},
}

Endnote

%0 Journal Article
%A Garg, Naveen
%A Kavitha, T.
%A Kumar, Amit
%A Mehlhorn, Kurt
%A Mestre, Julián
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Assigning Papers to Referees :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1611-4
%F EDOC: 536729
%R 10.1007/s00453-009-9386-0
%U http://dx.doi.org/10.1007/s00453-009-9386-0
%F OTHER: Local-ID: C1256428004B93B8-213E0759D254F459C12576C500583EE4-MehlhonMestre2009
%7 2010
%D 2010
%* Review method: peer-reviewed
%J Algorithmica
%V 58
%N 1
%& 119
%P 119 - 136
%I Springer
%C New York, NY
%@ false

[146]

R. M. McConnell, K. Mehlhorn, S. Näher, and P. Schweitzer, “Certifying Algorithms,” Computer Science Review, vol. 5, no. 2, 2010.

Export

BibTeX

@article{McConnell2010,
TITLE = {Certifying Algorithms},
AUTHOR = {McConnell, Ross M. and Mehlhorn, Kurt and N{\"a}her, Stefan and Schweitzer, Pascal},
LANGUAGE = {eng},
ISSN = {1574-0137},
URL = {http://dx.doi.org/10.1016/j.cosrev.2010.09.009},
DOI = {10.1016/j.cosrev.2010.09.009},
LOCALID = {Local-ID: C1256428004B93B8-3814D1CC91136BA8C1257846003BA54F-McConnell2010},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2010},
DATE = {2010},
JOURNAL = {Computer Science Review},
VOLUME = {5},
NUMBER = {2},
PAGES = {119--161},
}

Endnote

%0 Journal Article
%A McConnell, Ross M.
%A Mehlhorn, Kurt
%A Näher, Stefan
%A Schweitzer, Pascal
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1624-9
%F EDOC: 536711
%R 10.1016/j.cosrev.2010.09.009
%U http://dx.doi.org/10.1016/j.cosrev.2010.09.009
%F OTHER: Local-ID: C1256428004B93B8-3814D1CC91136BA8C1257846003BA54F-McConnell2010
%7 2010
%D 2010
%J Computer Science Review
%V 5
%N 2
%& 119
%P 119 - 161
%I Elsevier
%C Amsterdam
%@ false

[147]

K. Mehlhorn and P. Schweitzer, “Progress on Certifying Algorithms,” in Frontiers in Algorithmics (FAW 2010), Wuhan, China, 2010.

Export

BibTeX

@inproceedings{MehlhornSchweitzer2010,
TITLE = {Progress on Certifying Algorithms},
AUTHOR = {Mehlhorn, Kurt and Schweitzer, Pascal},
LANGUAGE = {eng},
ISBN = {978-3-642-14552-0},
URL = {http://dx.doi.org/10.1007/978-3-642-14553-7_1},
DOI = {10.1007/978-3-642-14553-7_1},
LOCALID = {Local-ID: C1256428004B93B8-6ADD7B6CDB83F33EC125781800375471-MehlhornSchweitzer2010},
PUBLISHER = {Springer},
YEAR = {2010},
DATE = {2010},
BOOKTITLE = {Frontiers in Algorithmics (FAW 2010)},
EDITOR = {Lee, Der-Tsai and Chen, Danny Z. and Ying, Shi},
PAGES = {1--5},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {6213},
ADDRESS = {Wuhan, China},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Schweitzer, Pascal
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Progress on Certifying Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-16C0-9
%F EDOC: 536774
%R 10.1007/978-3-642-14553-7_1
%U http://dx.doi.org/10.1007/978-3-642-14553-7_1
%F OTHER: Local-ID: C1256428004B93B8-6ADD7B6CDB83F33EC125781800375471-MehlhornSchweitzer2010
%D 2010
%B 4th International Workshop on Frontiers in Algorithmics
%Z date of event: 2010-08-11 - 2010-08-13
%C Wuhan, China
%B Frontiers in Algorithmics
%E Lee, Der-Tsai; Chen, Danny Z.; Ying, Shi
%P 1 - 5
%I Springer
%@ 978-3-642-14552-0
%B Lecture Notes in Computer Science
%N 6213

[148]

K. Mehlhorn and S. Ray, “Faster Algorithms for Computing Hong’s Bound on Absolute Positiveness,” Journal of Symbolic Computation, vol. 45, no. 6, 2010.

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BibTeX

@article{MehlhornRay2010,
TITLE = {Faster Algorithms for Computing Hong{\textquoteright}s Bound on Absolute Positiveness},
AUTHOR = {Mehlhorn, Kurt and Ray, Saurabh},
LANGUAGE = {eng},
ISSN = {0747-7171},
URL = {http://dx.doi.org/10.1016/j.jsc.2010.02.002},
DOI = {10.1016/j.jsc.2010.02.002},
LOCALID = {Local-ID: C1256428004B93B8-F2A3B1100AA47E69C125781800385310-MehlhornRay2010},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2010},
DATE = {2010},
JOURNAL = {Journal of Symbolic Computation},
VOLUME = {45},
NUMBER = {6},
PAGES = {677--683},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Ray, Saurabh
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Faster Algorithms for Computing Hong’s Bound on Absolute Positiveness :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1653-1
%F EDOC: 536776
%R 10.1016/j.jsc.2010.02.002
%U http://dx.doi.org/10.1016/j.jsc.2010.02.002
%F OTHER: Local-ID: C1256428004B93B8-F2A3B1100AA47E69C125781800385310-MehlhornRay2010
%7 2010
%D 2010
%* Review method: peer-reviewed
%J Journal of Symbolic Computation
%V 45
%N 6
%& 677
%P 677 - 683
%I Elsevier
%C Amsterdam
%@ false

[149]

K. Mehlhorn, “Reliable and Efficient Geometric Computing,” in Mathematical Software (ICMS 2010), Kobe, Japan, 2010.

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BibTeX

@inproceedings{Mehlhorn2010,
TITLE = {Reliable and Efficient Geometric Computing},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-642-15581-9},
URL = {http://dx.doi.org/10.1007/978-3-642-15582-6_3},
DOI = {10.1007/978-3-642-15582-6_3},
LOCALID = {Local-ID: C1256428004B93B8-ECD1954FEE1EB130C125781700444D74-Mehlhorn2010},
PUBLISHER = {Springer},
YEAR = {2010},
DATE = {2010},
BOOKTITLE = {Mathematical Software (ICMS 2010)},
EDITOR = {Fukuda, Komei and Van der Hoeven, Joris and Joswig, Michael and Takayama, Nobuki},
PAGES = {10--11},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {6327},
ADDRESS = {Kobe, Japan},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Reliable and Efficient Geometric Computing :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-16CC-2
%F EDOC: 536767
%R 10.1007/978-3-642-15582-6_3
%U http://dx.doi.org/10.1007/978-3-642-15582-6_3
%F OTHER: Local-ID: C1256428004B93B8-ECD1954FEE1EB130C125781700444D74-Mehlhorn2010
%D 2010
%B Third International Congress on Mathematical Software
%Z date of event: 2010-09-13 - 2010-09-17
%C Kobe, Japan
%B Mathematical Software
%E Fukuda, Komei; Van der Hoeven, Joris; Joswig, Michael; Takayama, Nobuki
%P 10 - 11
%I Springer
%@ 978-3-642-15581-9
%B Lecture Notes in Computer Science
%N 6327

2009

[150]

E. Amaldi, C. Iuliano, T. Jurkiewicz, K. Mehlhorn, and R. Rizzi, “Breaking the O(m^2n) Barrier for Minimum Cycle Bases,” in Algorithms - ESA 2009, Copenhagen, Denmark, 2009.

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BibTeX

@inproceedings{AmaldiIulianoetal009,
TITLE = {Breaking the {O(m^2n)} Barrier for Minimum Cycle Bases},
AUTHOR = {Amaldi, Edoardo and Iuliano, Claudio and Jurkiewicz, Tomasz and Mehlhorn, Kurt and Rizzi, Romeo},
LANGUAGE = {eng},
ISBN = {978-3-642-04127-3},
DOI = {10.1007/978-3-642-04128-0_28},
PUBLISHER = {Springer},
YEAR = {2009},
DATE = {2009},
BOOKTITLE = {Algorithms -- ESA 2009},
EDITOR = {Fiat, Amos and Sanders, Peter},
PAGES = {301--312},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {5757},
ADDRESS = {Copenhagen, Denmark},
}

Endnote

%0 Conference Proceedings
%A Amaldi, Edoardo
%A Iuliano, Claudio
%A Jurkiewicz, Tomasz
%A Mehlhorn, Kurt
%A Rizzi, Romeo
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Breaking the O(m^2n) Barrier for Minimum Cycle Bases :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-DA98-1
%R 10.1007/978-3-642-04128-0_28
%D 2009
%B 17th Annual European Symposium on Algorithms
%Z date of event: 2009-09-07 - 2009-09-09
%C Copenhagen, Denmark
%B Algorithms - ESA 2009
%E Fiat, Amos; Sanders, Peter
%P 301 - 312
%I Springer
%@ 978-3-642-04127-3
%B Lecture Notes in Computer Science
%N 5757

[151]

C. Burnikel, S. Funke, K. Mehlhorn, S. Schirra, and S. Schmitt, “A Separation Bound for Real Algebraic Expressions,” Algorithmica, vol. 55, 2009.

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BibTeX

@article{Burnikel_Algorithmica2009,
TITLE = {A Separation Bound for Real Algebraic Expressions},
AUTHOR = {Burnikel, Christoph and Funke, Stefan and Mehlhorn, Kurt and Schirra, Stefan and Schmitt, Susanne},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-007-9132-4},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York},
YEAR = {2009},
DATE = {2009},
JOURNAL = {Algorithmica},
VOLUME = {55},
PAGES = {14--28},
}

Endnote

%0 Journal Article
%A Burnikel, Christoph
%A Funke, Stefan
%A Mehlhorn, Kurt
%A Schirra, Stefan
%A Schmitt, Susanne
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Separation Bound for Real Algebraic Expressions :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-002B-4E36-9
%R 10.1007/s00453-007-9132-4
%7 2007
%D 2009
%J Algorithmica
%V 55
%& 14
%P 14 - 28
%I Springer-Verlag
%C New York
%@ false

[152]

T. Kavitha, C. Liebchen, K. Mehlhorn, D. Michail, R. Rizzi, T. Ueckerdt, and K. Zweig, “Cycle Bases in Graphs: Characterization, Algorithms, Complexity, and Applications,” Computer Science Review, vol. 3, no. 4, 2009.

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BibTeX

@article{SurveyCycleBases,
TITLE = {Cycle Bases in Graphs: Characterization, Algorithms, Complexity, and Applications},
AUTHOR = {Kavitha, T. and Liebchen, Ch. and Mehlhorn, Kurt and Michail, Dimitrios and Rizzi, R. and Ueckerdt, T. and Zweig, K.},
LANGUAGE = {eng},
DOI = {10.1016/j.cosrev.2009.08.001},
LOCALID = {Local-ID: C1256428004B93B8-804B2DD468A04320C1257585005C05FE-SurveyCycleBases},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2009},
DATE = {2009},
JOURNAL = {Computer Science Review},
VOLUME = {3},
NUMBER = {4},
PAGES = {199--243},
}

Endnote

%0 Journal Article
%A Kavitha, T.
%A Liebchen, Ch.
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Rizzi, R.
%A Ueckerdt, T.
%A Zweig, K.
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
%T Cycle Bases in Graphs: Characterization, Algorithms, Complexity, and Applications :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1829-2
%F EDOC: 518293
%F OTHER: Local-ID: C1256428004B93B8-804B2DD468A04320C1257585005C05FE-SurveyCycleBases
%R 10.1016/j.cosrev.2009.08.001
%D 2009
%J Computer Science Review
%V 3
%N 4
%& 199
%P 199 - 243
%I Elsevier
%C Amsterdam

[153]

K. Mehlhorn and D. Michail, “Minimum Cycle Bases: Faster and Simpler,” ACM Transactions on Algorithms, vol. 6, no. 1, 2009.

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BibTeX

@article{CycleBasisSimplified,
TITLE = {Minimum Cycle Bases: Faster and Simpler},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
ISSN = {1549-6325},
DOI = {10.1145/1644015.1644023},
LOCALID = {Local-ID: C1256428004B93B8-2A4064B111CA0E04C1257585005CC8E1-CycleBasisSimplified},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2009},
DATE = {2009},
JOURNAL = {ACM Transactions on Algorithms},
VOLUME = {6},
NUMBER = {1},
PAGES = {8:1--8:13},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Minimum Cycle Bases: Faster and Simpler :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-187C-6
%F EDOC: 518294
%F OTHER: Local-ID: C1256428004B93B8-2A4064B111CA0E04C1257585005CC8E1-CycleBasisSimplified
%R 10.1145/1644015.1644023
%D 2009
%* Review method: peer-reviewed
%J ACM Transactions on Algorithms
%O TALG
%V 6
%N 1
%& 8:1
%P 8:1 - 8:13
%I ACM
%C New York, NY
%@ false

[154]

K. Mehlhorn and M. Sagraloff, “Isolating Real Roots of Real Polynomials,” Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation (ISSAC 2009). ACM, New York, NY, 2009.

Abstract

We describe a Descartes algorithm for root
isolation of polynomials with real coefficients. It is assumed that
the coefficients of the polynomial can be approximated with arbitrary
precision; exact
computation in the field of coefficients is not required. We refer to such
coefficients as bitstream coefficients. The algorithm is
deterministic and has almost the same asymptotic complexity as the
randomized bitstream-Descartes algorithm of~\citet{BitstreamDescartes}. Besides
being deterministic, the algorithm is also somewhat simpler
to analyze.

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BibTeX

@misc{ms-detbitdesc-09,
TITLE = {Isolating Real Roots of Real Polynomials},
AUTHOR = {Mehlhorn, Kurt and Sagraloff, Michael},
LANGUAGE = {eng},
ISBN = {978-1-60558-609-0},
DOI = {10.1145/1576702.1576737},
LOCALID = {Local-ID: C1256428004B93B8-AE8C9A24B63BC4A8C125759E0029B4A4-ms-detbitdesc-09},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2009},
DATE = {2009},
ABSTRACT = {We describe a Descartes algorithm for root isolation of polynomials with real coefficients. It is assumed that the coefficients of the polynomial can be approximated with arbitrary precision; exact computation in the field of coefficients is not required. We refer to such coefficients as bitstream coefficients. The algorithm is deterministic and has almost the same asymptotic complexity as the randomized bitstream-Descartes algorithm of~\citet{BitstreamDescartes}. Besides being deterministic, the algorithm is also somewhat simpler to analyze.},
BOOKTITLE = {Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation (ISSAC 2009)},
PAGES = {247--254},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Sagraloff, Michael
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Isolating Real Roots of Real Polynomials :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-17F2-2
%F EDOC: 518292
%F OTHER: Local-ID: C1256428004B93B8-AE8C9A24B63BC4A8C125759E0029B4A4-ms-detbitdesc-09
%R 10.1145/1576702.1576737
%D 2009
%B 2009 International Symposium on Symbolic and Algebraic Computation
%Z date of event: 2009-07-28 - 2009-07-31
%C Seoul, Korea
%X We describe a Descartes algorithm for root
isolation of polynomials with real coefficients. It is assumed that
the coefficients of the polynomial can be approximated with arbitrary
precision; exact
computation in the field of coefficients is not required. We refer to such
coefficients as bitstream coefficients. The algorithm is
deterministic and has almost the same asymptotic complexity as the
randomized bitstream-Descartes algorithm of~\citet{BitstreamDescartes}. Besides
being deterministic, the algorithm is also somewhat simpler
to analyze.
%B Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
%P 247 - 254
%I ACM
%@ 978-1-60558-609-0

[155]

N. Sherashidze, S. V. N. Vishwanathan, T. H. Petri, K. Mehlhorn, and K. M. Borgwardt, “Efficient Graphlet Kernels for Large Graph Comparison,” in 12th International Conference on Artificial Intelligence and Statistics (AISTATS 2009), Clearwater Beach, FL, USA, 2009.

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BibTeX

@inproceedings{Graphlets,
TITLE = {Efficient Graphlet Kernels for Large Graph Comparison},
AUTHOR = {Sherashidze, Nino and Vishwanathan, S. V. N. and Petri, Tobias H. and Mehlhorn, Kurt and Borgwardt, Karsten M.},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-43BA02F2485CFBF4C1257585005B4454-Graphlets},
PUBLISHER = {Society for Artificial Intelligence and Statistics},
YEAR = {2009},
DATE = {2009},
BOOKTITLE = {12th International Conference on Artificial Intelligence and Statistics (AISTATS 2009)},
EDITOR = {van Dyk, David and Welling, Max},
PAGES = {488--495},
SERIES = {Proceedings of Machine Learning Research},
VOLUME = {5},
ADDRESS = {Clearwater Beach, FL, USA},
}

Endnote

%0 Conference Proceedings
%A Sherashidze, Nino
%A Vishwanathan, S. V. N.
%A Petri, Tobias H.
%A Mehlhorn, Kurt
%A Borgwardt, Karsten M.
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Efficient Graphlet Kernels for Large Graph Comparison :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1834-8
%F EDOC: 518242
%F OTHER: Local-ID: C1256428004B93B8-43BA02F2485CFBF4C1257585005B4454-Graphlets
%D 2009
%B 12th International Conference on Artificial Intelligence and Statistics
%Z date of event: 2009-03-26 - 2009-03-26
%C Clearwater Beach, FL, USA
%B 12th International Conference on Artificial Intelligence and Statistics
%E van Dyk, David; Welling, Max
%P 488 - 495
%I Society for Artificial Intelligence and Statistics
%B Proceedings of Machine Learning Research
%N 5
%U http://proceedings.mlr.press/v5/shervashidze09a/shervashidze09a.pdf

2008

[156]

S. Angelopoulos, “A Near-Tight Bound for the Online Steiner Tree Problem in Graphs of Bounded Asymmetry,” in Algorithms - ESA 2008, Karlsruhe, Germany, 2008, pp. 76–87.

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BibTeX

@inproceedings{Ang:08.steiner,
TITLE = {A Near-Tight Bound for the Online Steiner Tree Problem in Graphs of Bounded Asymmetry},
AUTHOR = {Angelopoulos, Spyros},
LANGUAGE = {eng},
ISBN = {978-3-540-87743-1},
DOI = {10.1007/978-3-540-87744-8_7},
LOCALID = {Local-ID: C125756E0038A185-3EB6F5B2FD7D2467C1257551004AD9C1-Ang:08.steiner},
PUBLISHER = {Springer},
YEAR = {2008},
DATE = {2008},
BOOKTITLE = {Algorithms -- ESA 2008},
EDITOR = {Halperin, Dan and Mehlhorn, Kurt},
PAGES = {76--87},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {5193},
ADDRESS = {Karlsruhe, Germany},
}

Endnote

%0 Conference Proceedings
%A Angelopoulos, Spyros
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Near-Tight Bound for the Online Steiner Tree Problem in Graphs of Bounded Asymmetry :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1ADF-9
%F EDOC: 427974
%R 10.1007/978-3-540-87744-8_7
%F OTHER: Local-ID: C125756E0038A185-3EB6F5B2FD7D2467C1257551004AD9C1-Ang:08.steiner
%D 2008
%B 16th Annual European Symposium on
%Z date of event: 2008-09-15 - 2008-09-17
%C Karlsruhe, Germany
%B Algorithms - ESA 2008
%E Halperin, Dan; Mehlhorn, Kurt
%P 76 - 87
%I Springer
%@ 978-3-540-87743-1
%B Lecture Notes in Computer Science
%N 5193

[157]

G. Christodoulou, E. Koutsoupias, and A. Vidali, “A Characterization of 2-Player Mechanisms for Scheduling,” in Algorithms - ESA 2008, Karlsruhe, Germany, 2008.

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BibTeX

@inproceedings{ChristodoulouKV2008,
TITLE = {A Characterization of 2-Player Mechanisms for Scheduling},
AUTHOR = {Christodoulou, George and Koutsoupias, Elias and Vidali, Angelina},
LANGUAGE = {eng},
ISBN = {978-3-540-87743-1},
DOI = {10.1007/978-3-540-87744-8},
LOCALID = {Local-ID: C125756E0038A185-2E4C37A8576707E2C125753A006C38D1-ChristodoulouKV2008},
PUBLISHER = {Springer},
YEAR = {2008},
DATE = {2008},
BOOKTITLE = {Algorithms -- ESA 2008},
EDITOR = {Halperin, Dan and Mehlhorn, Kurt},
PAGES = {297--307},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {5193},
ADDRESS = {Karlsruhe, Germany},
}

Endnote

%0 Conference Proceedings
%A Christodoulou, George
%A Koutsoupias, Elias
%A Vidali, Angelina
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Characterization of 2-Player Mechanisms for Scheduling :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1ABE-4
%F EDOC: 428015
%R 10.1007/978-3-540-87744-8
%F OTHER: Local-ID: C125756E0038A185-2E4C37A8576707E2C125753A006C38D1-ChristodoulouKV2008
%D 2008
%B 16th Annual European Symposium on Algorithms
%Z date of event: 2008-09-15 - 2008-09-17
%C Karlsruhe, Germany
%B Algorithms - ESA 2008
%E Halperin, Dan; Mehlhorn, Kurt
%P 297 - 307
%I Springer
%@ 978-3-540-87743-1
%B Lecture Notes in Computer Science
%N 5193

[158]

D. Halperin and K. Mehlhorn, Eds., Algorithms - ESA 2008 : 16th Annual European Symposium. Springer, 2008.

Export

BibTeX

@proceedings{Mehlhorn08,
TITLE = {Algorithms -- ESA 2008 : 16th Annual European Symposium},
EDITOR = {Halperin, Dan and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {978-3-540-87743-1},
DOI = {10.1007/978-3-540-87744-8},
LOCALID = {Local-ID: C125756E0038A185-14FFC212583C3355C1257571003AEB16-Mehlhorn08},
PUBLISHER = {Springer},
YEAR = {2008},
DATE = {2008},
PAGES = {XVII, 844},
ADDRESS = {Karlsruhe, Germany},
}

Endnote

%0 Conference Proceedings
%E Halperin, Dan
%E Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Algorithms - ESA 2008 : 16th Annual European Symposium :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1AD1-5
%F EDOC: 428098
%@ 978-3-540-87743-1
%R 10.1007/978-3-540-87744-8
%F OTHER: Local-ID: C125756E0038A185-14FFC212583C3355C1257571003AEB16-Mehlhorn08
%I Springer
%D 2008
%B 16th Annual European Symposium on Algorithms
%Z date of event: 2008-09-15 - 2008-09-17
%D 2008
%C Karlsruhe, Germany
%P XVII, 844

[159]

R. Hariharan, T. Kavitha, and K. Mehlhorn, “Faster Algorithms for Minimum Cycle Basis in Directed Graphs,” SIAM Journal on Computing, vol. 38, no. 4, 2008.

Export

BibTeX

@article{Hariharan2008,
TITLE = {Faster Algorithms for Minimum Cycle Basis in Directed Graphs},
AUTHOR = {Hariharan, Ramesh and Kavitha, Telikepalli and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0097-5397},
URL = {http://dx.doi.org/10.1137/060670730},
DOI = {10.1137/060670730},
LOCALID = {Local-ID: C125756E0038A185-790E08A3736682E2C125757800338B00-Hariharan2008},
PUBLISHER = {SIAM},
ADDRESS = {Philadelphia, PA},
YEAR = {2008},
DATE = {2008},
JOURNAL = {SIAM Journal on Computing},
VOLUME = {38},
NUMBER = {4},
PAGES = {1430--1447},
}

Endnote

%0 Journal Article
%A Hariharan, Ramesh
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Faster Algorithms for Minimum Cycle Basis in Directed Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1BA5-1
%F EDOC: 428101
%R 10.1137/060670730
%U http://dx.doi.org/10.1137/060670730
%F OTHER: Local-ID: C125756E0038A185-790E08A3736682E2C125757800338B00-Hariharan2008
%7 2008
%D 2008
%* Review method: peer-reviewed
%J SIAM Journal on Computing
%V 38
%N 4
%& 1430
%P 1430 - 1447
%I SIAM
%C Philadelphia, PA
%@ false

[160]

T. Kavitha, K. Mehlhorn, D. Michail, and K. E. Paluch, “An O˜ (m2n) Algorithm for Minimum Cycle Basis of Graphs,” Algorithmica, vol. 52, no. 3, 2008.

Export

BibTeX

@article{Kavitha2008,
TITLE = {An O{\~{}} (m2n) Algorithm for Minimum Cycle Basis of Graphs},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios and Paluch, Katarzyna E.},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-007-9064-z},
LOCALID = {Local-ID: C125756E0038A185-7AA9BDC617A56BE7C125757800420759-Kavitha2008},
PUBLISHER = {Springer},
ADDRESS = {New York},
YEAR = {2008},
DATE = {2008},
JOURNAL = {Algorithmica},
VOLUME = {52},
NUMBER = {3},
PAGES = {333--349},
}

Endnote

%0 Journal Article
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Paluch, Katarzyna E.
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T An O˜ (m2n) Algorithm for Minimum Cycle Basis of Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1AEB-D
%F EDOC: 428121
%R 10.1007/s00453-007-9064-z
%F OTHER: Local-ID: C125756E0038A185-7AA9BDC617A56BE7C125757800420759-Kavitha2008
%7 2008
%D 2008
%* Review method: peer-reviewed
%J Algorithmica
%V 52
%N 3
%& 333
%P 333 - 349
%I Springer
%C New York
%@ false

[161]

L. Kettner, K. Mehlhorn, S. Pion, S. Schirra, and C. Yap, “Classroom Examples of Robustness Problems in Geometric Computations,” Computational Geometry: Theory and Applications, vol. 40, no. 1, 2008.

Export

BibTeX

@article{Kettner2008_Classroom,
TITLE = {Classroom Examples of Robustness Problems in Geometric Computations},
AUTHOR = {Kettner, Lutz and Mehlhorn, Kurt and Pion, Sylvain and Schirra, Stefan and Yap, Chee},
LANGUAGE = {eng},
ISSN = {0925-7721},
URL = {http://dx.doi.org/10.1016/j.comgeo.2007.06.003},
DOI = {10.1016/j.comgeo.2007.06.003},
LOCALID = {Local-ID: C125756E0038A185-113F896EB9E35B7AC12573E60045601C-Kettner2007Classroom},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2008},
DATE = {2008},
JOURNAL = {Computational Geometry: Theory and Applications},
VOLUME = {40},
NUMBER = {1},
PAGES = {61--78},
}

Endnote

%0 Journal Article
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Pion, Sylvain
%A Schirra, Stefan
%A Yap, Chee
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Classroom Examples of Robustness Problems in Geometric Computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1B35-C
%F EDOC: 428123
%R 10.1016/j.comgeo.2007.06.003
%U http://dx.doi.org/10.1016/j.comgeo.2007.06.003
%F OTHER: Local-ID: C125756E0038A185-113F896EB9E35B7AC12573E60045601C-Kettner2007Classroom
%7 2008
%D 2008
%* Review method: peer-reviewed
%J Computational Geometry: Theory and Applications
%V 40
%N 1
%& 61
%P 61 - 78
%I Elsevier
%C Amsterdam
%@ false

[162]

K. Mehlhorn and P. Sanders, Algorithms and Data Structures: The Basic Toolbox. Berlin: Springer, 2008.

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BibTeX

@book{Mehlhorn-Sanders:Toolbox,
TITLE = {Algorithms and Data Structures: The Basic Toolbox},
AUTHOR = {Mehlhorn, Kurt and Sanders, Peter},
LANGUAGE = {eng},
ISBN = {978-3-540-77977-3},
DOI = {10.1007/978-3-540-77978-0},
LOCALID = {Local-ID: C1256428004B93B8-75AD1CF772C0FE5BC12575850043645F-Mehlhorn-Sanders:Toolbox},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {2008},
DATE = {2008},
PAGES = {300},
}

Endnote

%0 Book
%A Mehlhorn, Kurt
%A Sanders, Peter
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Algorithms and Data Structures: The Basic Toolbox :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-17F9-3
%F EDOC: 518298
%R 10.1007/978-3-540-77978-0
%@ 978-3-540-77977-3
%F OTHER: Local-ID: C1256428004B93B8-75AD1CF772C0FE5BC12575850043645F-Mehlhorn-Sanders:Toolbox
%I Springer
%C Berlin
%D 2008
%P 300

[163]

K. Mehlhorn, “Faster Deterministic and Randomized Algorithms for Minimum Cycle Basis in Directed Graphs,” SIAM Journal of Computing, vol. 38, no. 4, 2008.

Export

BibTeX

@article{Mehlhorn2008b,
TITLE = {Faster Deterministic and Randomized Algorithms for Minimum Cycle Basis in Directed Graphs},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1042-9832},
URL = {http://www.mpi-inf.mpg.de/~mehlhorn/ftp/DirectedCycleBasisJournal.pdf},
DOI = {10.1137/060670730},
LOCALID = {Local-ID: C125756E0038A185-2E4A966E27BF5CF7C125755B004DA137-Mehlhorn2008b},
YEAR = {2008},
DATE = {2008},
JOURNAL = {SIAM Journal of Computing},
VOLUME = {38},
NUMBER = {4},
PAGES = {1430--1447},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Faster Deterministic and Randomized Algorithms for Minimum Cycle Basis in Directed Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1BA7-E
%F EDOC: 428164
%U http://www.mpi-inf.mpg.de/~mehlhorn/ftp/DirectedCycleBasisJournal.pdf
%F OTHER: Local-ID: C125756E0038A185-2E4A966E27BF5CF7C125755B004DA137-Mehlhorn2008b
%R 10.1137/060670730
%D 2008
%* Review method: peer-reviewed
%J SIAM Journal of Computing
%V 38
%N 4
%& 1430
%P 1430 - 1447
%@ false

2007

[164]

D. J. Abraham, R. W. Irving, T. Kavitha, and K. Mehlhorn, “Popular Matchings,” SIAM Journal on Computing, vol. 37, no. 4, 2007.

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BibTeX

@article{Abraham2007Popular,
TITLE = {Popular Matchings},
AUTHOR = {Abraham, David J. and Irving, Robert W. and Kavitha, Telikepalli and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0097-5397},
DOI = {10.1137/06067328X},
LOCALID = {Local-ID: C12573CC004A8E26-6B07E5D0BA1AD3E5C12573E70031E1C4-Abraham2007Popular},
PUBLISHER = {SIAM},
ADDRESS = {Philadelphia, PA},
YEAR = {2007},
DATE = {2007},
JOURNAL = {SIAM Journal on Computing},
VOLUME = {37},
NUMBER = {4},
PAGES = {1030--1045},
}

Endnote

%0 Journal Article
%A Abraham, David J.
%A Irving, Robert W.
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Popular Matchings :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2059-8
%F EDOC: 356652
%R 10.1137/06067328X
%F OTHER: Local-ID: C12573CC004A8E26-6B07E5D0BA1AD3E5C12573E70031E1C4-Abraham2007Popular
%7 2007
%D 2007
%* Review method: peer-reviewed
%J SIAM Journal on Computing
%V 37
%N 4
%& 1030
%P 1030 - 1045
%I SIAM
%C Philadelphia, PA
%@ false

[165]

E. Berberich, E. Fogel, D. Halperin, K. Mehlhorn, and R. Wein, “Sweeping and Maintaining two-dimensional Arrangements on Surfaces: A First Step,” in Algorithms - ESA 2007, Eilat, Israel, 2007.

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BibTeX

@inproceedings{bfhmw-samtdaosafs-07,
TITLE = {Sweeping and Maintaining two-dimensional Arrangements on Surfaces: A First Step},
AUTHOR = {Berberich, Eric and Fogel, Efi and Halperin, Dan and Mehlhorn, Kurt and Wein, Ron},
LANGUAGE = {eng},
ISBN = {978-3-540-75519-7},
DOI = {10.1007/978-3-540-75520-3_57},
LOCALID = {Local-ID: C12573CC004A8E26-5496A47512AF3FBEC12573D1004BD408-bfhmw-samtdaosafs-07},
PUBLISHER = {Springer},
YEAR = {2007},
DATE = {2007},
BOOKTITLE = {Algorithms -- ESA 2007},
EDITOR = {Arge, Lars and Hoffmann, Michael and Welzl, Emo},
PAGES = {645--656},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4698},
ADDRESS = {Eilat, Israel},
}

Endnote

%0 Conference Proceedings
%A Berberich, Eric
%A Fogel, Efi
%A Halperin, Dan
%A Mehlhorn, Kurt
%A Wein, Ron
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Sweeping and Maintaining two-dimensional Arrangements on Surfaces: A First Step :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-20E9-6
%F EDOC: 356662
%R 10.1007/978-3-540-75520-3_57
%F OTHER: Local-ID: C12573CC004A8E26-5496A47512AF3FBEC12573D1004BD408-bfhmw-samtdaosafs-07
%D 2007
%B 15th Annual European Symposium on Algorithms
%Z date of event: 2007-10-08 - 2007-10-10
%C Eilat, Israel
%B Algorithms - ESA 2007
%E Arge, Lars; Hoffmann, Michael; Welzl, Emo
%P 645 - 656
%I Springer
%@ 978-3-540-75519-7
%B Lecture Notes in Computer Science
%N 4698

[166]

E. Berberich, E. Fogel, D. Halperin, K. Mehlhorn, and R. Wein, “Sweeping and maintaining two-dimensional arrangements on quadrics,” University of Groningen, Groningen, The Netherlands, ACS-TR-241402-02, 2007.

Export

BibTeX

@techreport{acs:bfhmw-smtaoq-07,
TITLE = {Sweeping and maintaining two-dimensional arrangements on quadrics},
AUTHOR = {Berberich, Eric and Fogel, Efi and Halperin, Dan and Mehlhorn, Kurt and Wein, Ron},
LANGUAGE = {eng},
NUMBER = {ACS-TR-241402-02},
LOCALID = {Local-ID: C12573CC004A8E26-A2D9FC191F294C4BC12573D1004D4FA3-acs:bfhmw-smtaoq-07},
INSTITUTION = {University of Groningen},
ADDRESS = {Groningen, The Netherlands},
YEAR = {2007},
DATE = {2007},
TYPE = {ACS Technical Reports},
}

Endnote

%0 Report
%A Berberich, Eric
%A Fogel, Efi
%A Halperin, Dan
%A Mehlhorn, Kurt
%A Wein, Ron
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Sweeping and maintaining two-dimensional arrangements on quadrics :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-20E3-1
%F EDOC: 356692
%F OTHER: Local-ID: C12573CC004A8E26-A2D9FC191F294C4BC12573D1004D4FA3-acs:bfhmw-smtaoq-07
%Y University of Groningen
%C Groningen, The Netherlands
%D 2007
%P 10 p.
%B ACS Technical Reports

[167]

C. Gotsman, K. Kaligosi, K. Mehlhorn, D. Michail, and E. Pyrga, “Cycle Bases of Graphs and Sampled Manifolds,” Computer Aided Geometric Design, vol. 24, no. 8/9, 2007.

Export

BibTeX

@article{GKMMP06,
TITLE = {Cycle Bases of Graphs and Sampled Manifolds},
AUTHOR = {Gotsman, Craig and Kaligosi, Kanela and Mehlhorn, Kurt and Michail, Dimitrios and Pyrga, Evangelia},
LANGUAGE = {eng},
ISSN = {0167-8396},
DOI = {10.1016/j.cagd.2006.07.001},
LOCALID = {Local-ID: C12573CC004A8E26-CE8DCB4C127284AAC125728E003EFD6F-GKMMP06},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {2007},
DATE = {2007},
JOURNAL = {Computer Aided Geometric Design},
VOLUME = {24},
NUMBER = {8/9},
PAGES = {464--480},
}

Endnote

%0 Journal Article
%A Gotsman, Craig
%A Kaligosi, Kanela
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Pyrga, Evangelia
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Cycle Bases of Graphs and Sampled Manifolds :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1EC9-C
%F EDOC: 356742
%R 10.1016/j.cagd.2006.07.001
%F OTHER: Local-ID: C12573CC004A8E26-CE8DCB4C127284AAC125728E003EFD6F-GKMMP06
%7 2007
%D 2007
%* Review method: peer-reviewed
%J Computer Aided Geometric Design
%V 24
%N 8/9
%& 464
%P 464 - 480
%I North-Holland
%C Amsterdam
%@ false

[168]

P. Hachenberger, L. Kettner, and K. Mehlhorn, “Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, Optimized Implementation and Experiments,” Computational Geometry: Theory and Applications, vol. 38, no. 1–2, 2007.

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BibTeX

@article{Kettner2007Nef3,
TITLE = {Boolean Operations on 3{D} Selective Nef Complexes: Data Structure, Algorithms, Optimized Implementation and Experiments},
AUTHOR = {Hachenberger, Peter and Kettner, Lutz and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0925-7721},
DOI = {10.1016/j.comgeo.2006.11.009},
LOCALID = {Local-ID: C12573CC004A8E26-FECC77F07C1A1E72C12573D20003E1DD-Kettner2007Nef3},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2007},
DATE = {2007},
JOURNAL = {Computational Geometry: Theory and Applications},
VOLUME = {38},
NUMBER = {1-2},
PAGES = {64--99},
}

Endnote

%0 Journal Article
%A Hachenberger, Peter
%A Kettner, Lutz
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, Optimized Implementation and Experiments :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1E75-A
%F EDOC: 356713
%R 10.1016/j.comgeo.2006.11.009
%F OTHER: Local-ID: C12573CC004A8E26-FECC77F07C1A1E72C12573D20003E1DD-Kettner2007Nef3
%7 2007
%D 2007
%* Review method: peer-reviewed
%J Computational Geometry: Theory and Applications
%V 38
%N 1-2
%& 64
%P 64 - 99
%I Elsevier
%C Amsterdam
%@ false

[169]

T. Kavitha, K. Mehlhorn, D. Michail, and K. E. Paluch, “Strongly Stable Matchings in Time O(nm) and Extension to the Hospitals-residents Problem,” ACM Transactions on Algorithms, vol. 3, no. 2, 2007.

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BibTeX

@article{a15-kavitha,
TITLE = {Strongly Stable Matchings in Time O(nm) and Extension to the Hospitals-residents Problem},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios and Paluch, Katarzyna E.},
LANGUAGE = {eng},
ISSN = {1549-6325},
DOI = {10.1145/1240233.1240238},
LOCALID = {Local-ID: C12573CC004A8E26-C2986B86FD6341EBC12573CA0030895C-a15-kavitha},
PUBLISHER = {ACM},
ADDRESS = {New York, NY},
YEAR = {2007},
DATE = {2007},
JOURNAL = {ACM Transactions on Algorithms},
VOLUME = {3},
NUMBER = {2},
PAGES = {15.1--15.18},
}

Endnote

%0 Journal Article
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Paluch, Katarzyna E.
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Strongly Stable Matchings in Time O(nm) and Extension to the Hospitals-residents Problem :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-20CE-4
%F EDOC: 356670
%R 10.1145/1240233.1240238
%F OTHER: Local-ID: C12573CC004A8E26-C2986B86FD6341EBC12573CA0030895C-a15-kavitha
%7 2007
%D 2007
%* Review method: peer-reviewed
%J ACM Transactions on Algorithms
%V 3
%N 2
%& 15.1
%P 15.1 - 15.18
%I ACM
%C New York, NY
%@ false

[170]

T. Kavitha, K. Mehlhorn, and D. Michail, “New Approximation Algorithms for Minimum Cycle Bases of Graphs,” in STACS 2007, Aachen, Germany, 2007.

Abstract

We consider the problem of computing an approximate minimum cycle basis of an
undirected edge-weighted graph G with m edges and n vertices; the extension to
directed graphs is also discussed. In this problem, a {0,1} incidence vector is
associated with each cycle and the vector space over generated by these vectors
is the cycle space of G. A set of cycles is called a cycle basis of G if it
forms a basis for its cycle space. A cycle basis where the sum of the weights
of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of
low weight are useful in a number of contexts, e.g. the analysis of electrical
networks, structural engineering, chemistry, and surface reconstruction.
We present two new algorithms to compute an approximate minimum cycle basis.
For any integer k ≥ 1, we give (2k − 1)-approximation algorithms with expected
running time O(k m n1 + 2/k + m n(1 + 1/k)(ω − 1)) and deterministic running
time O( n3 + 2/k ), respectively. Here ω is the best exponent of matrix
multiplication. It is presently known that ω < 2.376. Both algorithms are o( mω
) for dense graphs. This is the first time that any algorithm which computes
sparse cycle bases with a guarantee drops below the Θ(mω) bound.
We also present a 2-approximation algorithm with expected running time, a
linear time 2-approximation algorithm for planar graphs and an O(n3) time
2.42-approximation algorithm for the complete Euclidean graph in the plane.

Export

BibTeX

@inproceedings{KMM07,
TITLE = {New Approximation Algorithms for Minimum Cycle Bases of Graphs},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
ISBN = {978-3-540-70917-6},
DOI = {10.1007/978-3-540-70918-3_44},
LOCALID = {Local-ID: C12573CC004A8E26-2BFAB74EC24AD32DC125728E003EAFF1-KMM07},
PUBLISHER = {Springer},
YEAR = {2007},
DATE = {2007},
ABSTRACT = {We consider the problem of computing an approximate minimum cycle basis of an undirected edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of the weights of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of low weight are useful in a number of contexts, e.g. the analysis of electrical networks, structural engineering, chemistry, and surface reconstruction. We present two new algorithms to compute an approximate minimum cycle basis. For any integer k\,$\geq$\,1, we give (2k\,{\textminus}\,1)-approximation algorithms with expected running time O(k m n1\,+\,2/k\,+\,m n(1\,+\,1/k)($\omega$\,{\textminus}\,1)) and deterministic running time O( n3\,+\,2/k ), respectively. Here $\omega$ is the best exponent of matrix multiplication. It is presently known that $\omega$\,<\,2.376. Both algorithms are o( m$\omega$ ) for dense graphs. This is the first time that any algorithm which computes sparse cycle bases with a guarantee drops below the $\Theta$(m$\omega$) bound. We also present a 2-approximation algorithm with expected running time, a linear time 2-approximation algorithm for planar graphs and an O(n3) time 2.42-approximation algorithm for the complete Euclidean graph in the plane.},
BOOKTITLE = {STACS 2007},
EDITOR = {Thomas, Wolfgang and Weil, Pascal},
PAGES = {512--523},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4393},
ADDRESS = {Aachen, Germany},
}

Endnote

%0 Conference Proceedings
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New Approximation Algorithms for Minimum Cycle Bases of Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2001-E
%F EDOC: 356750
%R 10.1007/978-3-540-70918-3_44
%F OTHER: Local-ID: C12573CC004A8E26-2BFAB74EC24AD32DC125728E003EAFF1-KMM07
%D 2007
%B 24th Annual Symposium on Theoretical Aspects of Computer Science
%Z date of event: 2007-02-22 - 2007-02-24
%C Aachen, Germany
%X We consider the problem of computing an approximate minimum cycle basis of an
undirected edge-weighted graph G with m edges and n vertices; the extension to
directed graphs is also discussed. In this problem, a {0,1} incidence vector is
associated with each cycle and the vector space over generated by these vectors
is the cycle space of G. A set of cycles is called a cycle basis of G if it
forms a basis for its cycle space. A cycle basis where the sum of the weights
of the cycles is minimum is called a minimum cycle basis of G. Cycle bases of
low weight are useful in a number of contexts, e.g. the analysis of electrical
networks, structural engineering, chemistry, and surface reconstruction.
We present two new algorithms to compute an approximate minimum cycle basis.
For any integer k ≥ 1, we give (2k − 1)-approximation algorithms with expected
running time O(k m n1 + 2/k + m n(1 + 1/k)(ω − 1)) and deterministic running
time O( n3 + 2/k ), respectively. Here ω is the best exponent of matrix
multiplication. It is presently known that ω < 2.376. Both algorithms are o( mω
) for dense graphs. This is the first time that any algorithm which computes
sparse cycle bases with a guarantee drops below the Θ(mω) bound.
We also present a 2-approximation algorithm with expected running time, a
linear time 2-approximation algorithm for planar graphs and an O(n3) time
2.42-approximation algorithm for the complete Euclidean graph in the plane.
%B STACS 2007
%E Thomas, Wolfgang; Weil, Pascal
%P 512 - 523
%I Springer
%@ 978-3-540-70917-6
%B Lecture Notes in Computer Science
%N 4393

[171]

T. Kavitha and K. Mehlhorn, “Algorithms to Compute Minimum Cycle Basis in Directed Graphs,” Theory of Computing Systems, vol. 40, no. 4, 2007.

Export

BibTeX

@article{Kavitha2007TCS,
TITLE = {Algorithms to Compute Minimum Cycle Basis in Directed Graphs},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1432-4350},
DOI = {10.1007/s00224-006-1319-6},
LOCALID = {Local-ID: C12573CC004A8E26-4000DCDBCE376944C12573E6004AC629-Kavitha2007TCS},
PUBLISHER = {Springer},
ADDRESS = {New York, NY},
YEAR = {2007},
DATE = {2007},
JOURNAL = {Theory of Computing Systems},
VOLUME = {40},
NUMBER = {4},
PAGES = {485--505},
}

Endnote

%0 Journal Article
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Algorithms to Compute Minimum Cycle Basis in Directed Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1E02-A
%F EDOC: 356646
%R 10.1007/s00224-006-1319-6
%F OTHER: Local-ID: C12573CC004A8E26-4000DCDBCE376944C12573E6004AC629-Kavitha2007TCS
%7 2007
%D 2007
%* Review method: peer-reviewed
%J Theory of Computing Systems
%V 40
%N 4
%& 485
%P 485 - 505
%I Springer
%C New York, NY
%@ false

[172]

K. Mehlhorn and D. Michail, “Implementing Minimum Cycle Basis Algorithms,” Journal of Experimental Algorithmics, vol. 11, 2007.

Abstract

In this paper, we consider the problem of computing a minimum cycle basis of an
undirected graph G = (V,E) with n vertices and m edges. We describe an
efficient implementation of an O(m3 + mn2 log n) algorithm. For sparse
graphs, this is the currently best-known algorithm. This algorithm's running
time can be partitioned into two parts with time O(m3) and O(m2n + mn2 log
n), respectively. Our experimental findings imply that for random graphs the
true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log
n) part. A straightforward implementation would require Ω(nm) shortest-path
computations. Thus, we develop several heuristics in order to get a practical
algorithm. Our experiments show that in random graphs our techniques result in
a significant speed-up. Based on our experimental observations, we combine the
two fundamentally different approaches to compute a minimum cycle basis to
obtain a new hybrid algorithm with running time O(m2n2). The hybrid algorithm
is very efficient, in practice, for random dense unweighted graphs. Finally, we
compare these two algorithms with a number of previous implementations for
finding a minimum cycle basis of an undirected graph.

Export

BibTeX

@article{Mehlhorn2007b,
TITLE = {Implementing Minimum Cycle Basis Algorithms},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
ISSN = {1084-6654},
DOI = {10.1145/1187436.1216582},
LOCALID = {Local-ID: C12573CC004A8E26-7809D4DD4F26C131C125729C0046E9A4-Mehlhorn2007b},
PUBLISHER = {ACM},
ADDRESS = {New York, N.Y.},
YEAR = {2007},
DATE = {2007},
ABSTRACT = {In this paper, we consider the problem of computing a minimum cycle basis of an undirected graph G = (V,E) with n vertices and m edges. We describe an efficient implementation of an O(m3 + mn2 log n) algorithm. For sparse graphs, this is the currently best-known algorithm. This algorithm's running time can be partitioned into two parts with time O(m3) and O(m2n + mn2 log n), respectively. Our experimental findings imply that for random graphs the true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log n) part. A straightforward implementation would require $\Omega$(nm) shortest-path computations. Thus, we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speed-up. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis to obtain a new hybrid algorithm with running time O(m2n2). The hybrid algorithm is very efficient, in practice, for random dense unweighted graphs. Finally, we compare these two algorithms with a number of previous implementations for finding a minimum cycle basis of an undirected graph.},
JOURNAL = {Journal of Experimental Algorithmics},
VOLUME = {11},
PAGES = {2.5.1--2-5-14},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Implementing Minimum Cycle Basis Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1F7F-E
%F EDOC: 356694
%R 10.1145/1187436.1216582
%F OTHER: Local-ID: C12573CC004A8E26-7809D4DD4F26C131C125729C0046E9A4-Mehlhorn2007b
%7 2007
%D 2007
%X In this paper, we consider the problem of computing a minimum cycle basis of an
undirected graph G = (V,E) with n vertices and m edges. We describe an
efficient implementation of an O(m3 + mn2 log n) algorithm. For sparse
graphs, this is the currently best-known algorithm. This algorithm's running
time can be partitioned into two parts with time O(m3) and O(m2n + mn2 log
n), respectively. Our experimental findings imply that for random graphs the
true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log
n) part. A straightforward implementation would require Ω(nm) shortest-path
computations. Thus, we develop several heuristics in order to get a practical
algorithm. Our experiments show that in random graphs our techniques result in
a significant speed-up. Based on our experimental observations, we combine the
two fundamentally different approaches to compute a minimum cycle basis to
obtain a new hybrid algorithm with running time O(m2n2). The hybrid algorithm
is very efficient, in practice, for random dense unweighted graphs. Finally, we
compare these two algorithms with a number of previous implementations for
finding a minimum cycle basis of an undirected graph.
%J Journal of Experimental Algorithmics
%V 11
%& 2.5.1
%P 2.5.1 - 2-5-14
%I ACM
%C New York, N.Y.
%@ false

[173]

K. Mehlhorn, “Minimum Cycle Bases in Graphs Algorithms and Applications,” in Mathematical Foundations of Computer Science 2007 : 32nd International Symposium, MFCS 2007, 2007.

Export

BibTeX

@inproceedings{MehlhornMFCS07,
TITLE = {Minimum Cycle Bases in Graphs Algorithms and Applications},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-74455-9},
DOI = {10.1007/978-3-540-74456-6_3},
LOCALID = {Local-ID: C12573CC004A8E26-3E9ED811EBD4E1E9C12573FB002FFF04-MehlhornMFCS07},
PUBLISHER = {Springer},
YEAR = {2007},
DATE = {2007},
BOOKTITLE = {Mathematical Foundations of Computer Science 2007 : 32nd International Symposium, MFCS 2007},
EDITOR = {Kucera, Ludek and Kucera, Anton{\'i}n},
PAGES = {13--14},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4708},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Minimum Cycle Bases in Graphs Algorithms and Applications :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1FE2-A
%F EDOC: 356655
%R 10.1007/978-3-540-74456-6_3
%F OTHER: Local-ID: C12573CC004A8E26-3E9ED811EBD4E1E9C12573FB002FFF04-MehlhornMFCS07
%D 2007
%B Untitled Event
%Z date of event: 2007-08-26 - 2007-08-31
%C Cˇ eský Krumlov, Czech Republic
%B Mathematical Foundations of Computer Science 2007 : 32nd International Symposium, MFCS 2007
%E Kucera, Ludek; Kucera, Antonín
%P 13 - 14
%I Springer
%@ 3-540-74455-9
%B Lecture Notes in Computer Science
%N 4708

[174]

K. Mehlhorn, “Matchings in Graphs Variations of the Problem,” in Combinatorial Optimization and Applications : First International Conference, COCOA 2007, 2007.

Export

BibTeX

@inproceedings{COCOA07,
TITLE = {Matchings in Graphs Variations of the Problem},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-73555-7},
DOI = {10.1007/978-3-540-73556-4_1},
LOCALID = {Local-ID: C12573CC004A8E26-8919E7EBB8E64B8EC12573FB00310490-COCOA07},
PUBLISHER = {Springer},
YEAR = {2007},
DATE = {2007},
BOOKTITLE = {Combinatorial Optimization and Applications : First International Conference, COCOA 2007},
EDITOR = {Dress, Andreas and Xu, Yinfeng and Zhu, Binhai},
PAGES = {1--2},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4616},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Matchings in Graphs Variations of the Problem :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-1FC9-4
%F EDOC: 356688
%R 10.1007/978-3-540-73556-4_1
%F OTHER: Local-ID: C12573CC004A8E26-8919E7EBB8E64B8EC12573FB00310490-COCOA07
%D 2007
%B Untitled Event
%Z date of event: 2007-08-14 - 2007-08-16
%C Xi’an, China
%B Combinatorial Optimization and Applications : First International Conference, COCOA 2007
%E Dress, Andreas; Xu, Yinfeng; Zhu, Binhai
%P 1 - 2
%I Springer
%@ 3-540-73555-7
%B Lecture Notes in Computer Science
%N 4616

2006

[175]

B. Aronov, T. Asano, N. Katoh, K. Mehlhorn, and T. Tokuyama, “Polyline Fitting of Planar Points under Min-sum Criteria,” International Journal of Computational Geometry and Applications, vol. 16, 2006.

Abstract

Fitting a curve of a certain type to a given set of points in the plane is a
basic problem in statistics and has numerous applications. We consider fitting
a polyline with k joints under the min-sum criteria with respect to L1- and L2
-metrics, which are more appropriate measures than uniform and Hausdorff
metrics in statistical context. We present efficient algorithms for the 1-joint
versions of the problem and fully polynomial-time approximation schemes for the
general k-joint versions.

Export

BibTeX

@article{mehlhorn06z,
TITLE = {Polyline Fitting of Planar Points under Min-sum Criteria},
AUTHOR = {Aronov, Boris and Asano, Tetsuo and Katoh, Naoki and Mehlhorn, Kurt and Tokuyama, Takeshi},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-4975B3F8D71B70D6C12571C500423733-mehlhorn06z},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {Fitting a curve of a certain type to a given set of points in the plane is a basic problem in statistics and has numerous applications. We consider fitting a polyline with k joints under the min-sum criteria with respect to L1- and L2 -metrics, which are more appropriate measures than uniform and Hausdorff metrics in statistical context. We present efficient algorithms for the 1-joint versions of the problem and fully polynomial-time approximation schemes for the general k-joint versions.},
JOURNAL = {International Journal of Computational Geometry and Applications},
VOLUME = {16},
PAGES = {97--116},
}

Endnote

%0 Journal Article
%A Aronov, Boris
%A Asano, Tetsuo
%A Katoh, Naoki
%A Mehlhorn, Kurt
%A Tokuyama, Takeshi
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Polyline Fitting of Planar Points under Min-sum Criteria :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-23BA-3
%F EDOC: 314580
%F OTHER: Local-ID: C1256428004B93B8-4975B3F8D71B70D6C12571C500423733-mehlhorn06z
%D 2006
%* Review method: peer-reviewed
%X Fitting a curve of a certain type to a given set of points in the plane is a
basic problem in statistics and has numerous applications. We consider fitting
a polyline with k joints under the min-sum criteria with respect to L1- and L2
-metrics, which are more appropriate measures than uniform and Hausdorff
metrics in statistical context. We present efficient algorithms for the 1-joint
versions of the problem and fully polynomial-time approximation schemes for the
general k-joint versions.
%J International Journal of Computational Geometry and Applications
%V 16
%& 97
%P 97 - 116

[176]

H. Bast, K. Mehlhorn, G. Schäfer, and H. Tamaki, “Matching Algorithms are Fast in Sparse Random Graphs,” Theory of Computing Systems, vol. 39, 2006.

Abstract

We present an improved average case analysis of the maximum cardinality
matching problem. We show that in a bipartite or general random graph on $n$
vertices, with high probability every non-maximum matching has an augmenting
path of length $O(\log n)$. This implies that augmenting path algorithms like
the Hopcroft--Karp algorithm for bipartite graphs and the Micali--Vazirani
algorithm for general graphs, which have a worst case running time of
$O(m\sqrt{n})$, run in time $O(m \log n)$ with high probability, where $m$ is
the number of edges in the graph. Motwani proved these results for random
graphs when the average degree is at least $\ln (n)$ [\emph{Average Case
Analysis of Algorithms for Matchings and Related Problems}, Journal of the ACM,
\textbf{41}(6), 1994]. Our results hold, if only the average degree is a large
enough constant. At the same time we simplify the analysis of Motwani.

Export

BibTeX

@article{BMST05,
TITLE = {Matching Algorithms are Fast in Sparse Random Graphs},
AUTHOR = {Bast, Holger and Mehlhorn, Kurt and Sch{\"a}fer, Guido and Tamaki, Hisao},
LANGUAGE = {eng},
ISSN = {1432-4350},
LOCALID = {Local-ID: C1256428004B93B8-257B5C3871441CAAC1256FC0004404AB-BMST05},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on $n$ vertices, with high probability every non-maximum matching has an augmenting path of length $O(\log n)$. This implies that augmenting path algorithms like the Hopcroft--Karp algorithm for bipartite graphs and the Micali--Vazirani algorithm for general graphs, which have a worst case running time of $O(m\sqrt{n})$, run in time $O(m \log n)$ with high probability, where $m$ is the number of edges in the graph. Motwani proved these results for random graphs when the average degree is at least $\ln (n)$ [\emph{Average Case Analysis of Algorithms for Matchings and Related Problems}, Journal of the ACM, \textbf{41}(6), 1994]. Our results hold, if only the average degree is a large enough constant. At the same time we simplify the analysis of Motwani.},
JOURNAL = {Theory of Computing Systems},
VOLUME = {39},
PAGES = {3--14},
}

Endnote

%0 Journal Article
%A Bast, Holger
%A Mehlhorn, Kurt
%A Schäfer, Guido
%A Tamaki, Hisao
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Matching Algorithms are Fast in Sparse Random Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2361-9
%F EDOC: 314609
%F OTHER: Local-ID: C1256428004B93B8-257B5C3871441CAAC1256FC0004404AB-BMST05
%D 2006
%* Review method: peer-reviewed
%X We present an improved average case analysis of the maximum cardinality
matching problem. We show that in a bipartite or general random graph on $n$
vertices, with high probability every non-maximum matching has an augmenting
path of length $O(\log n)$. This implies that augmenting path algorithms like
the Hopcroft--Karp algorithm for bipartite graphs and the Micali--Vazirani
algorithm for general graphs, which have a worst case running time of
$O(m\sqrt{n})$, run in time $O(m \log n)$ with high probability, where $m$ is
the number of edges in the graph. Motwani proved these results for random
graphs when the average degree is at least $\ln (n)$ [\emph{Average Case
Analysis of Algorithms for Matchings and Related Problems}, Journal of the ACM,
\textbf{41}(6), 1994]. Our results hold, if only the average degree is a large
enough constant. At the same time we simplify the analysis of Motwani.
%J Theory of Computing Systems
%V 39
%& 3
%P 3 - 14
%@ false

[177]

S. Funke, C. Klein, K. Mehlhorn, and S. Schmitt, “Controlled Perturbation for Delaunay Triangulations,” Algorithms for Complex Shapes with certified topology and numerics, Instituut voor Wiskunde en Informatica, Groningen, NETHERLANDS, ACS-TR-121103-03, 2006.

Export

BibTeX

@techreport{acstr123109-01,
TITLE = {Controlled Perturbation for Delaunay Triangulations},
AUTHOR = {Funke, Stefan and Klein, Christian and Mehlhorn, Kurt and Schmitt, Susanne},
LANGUAGE = {eng},
NUMBER = {ACS-TR-121103-03},
INSTITUTION = {Algorithms for Complex Shapes with certified topology and numerics},
ADDRESS = {Instituut voor Wiskunde en Informatica, Groningen, NETHERLANDS},
YEAR = {2006},
DATE = {2006},
}

Endnote

%0 Report
%A Funke, Stefan
%A Klein, Christian
%A Mehlhorn, Kurt
%A Schmitt, Susanne
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Controlled Perturbation for Delaunay Triangulations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0027-F72F-3
%Y Algorithms for Complex Shapes with certified topology and numerics
%C Instituut voor Wiskunde en Informatica, Groningen, NETHERLANDS
%D 2006

[178]

R. Hariharan, K. Telikepalli, and K. Mehlhorn, “A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs,” in Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I, 2006.

Abstract

We consider the problem of computing a minimum cycle basis in a directed graph.
The input to this problem is a directed graph G whose edges have non-negative
weights. A cycle in this graph is actually a cycle in the underlying undirected
graph with edges traversable in both directions. A {–1,0,1} edge incidence
vector is associated with each cycle: edges traversed by the cycle in the right
direction get 1 and edges traversed in the opposite direction get -1. The
vector space over generated by these vectors is the cycle space of G. A minimum
cycle basis is a set of cycles of minimum weight that span the cycle space of
G. The current fastest algorithm for computing a minimum cycle basis in a
directed graph with m edges and n vertices runs in time (where ω< 2.376 is the
exponent of matrix multiplication). Here we present an O(m3n + m2n2logn)
algorithm. We also slightly improve the running time of the current fastest
randomized algorithm from O(m2nlogn) to O(m2 n + mn2 logn).

Export

BibTeX

@inproceedings{HTM06a,
TITLE = {A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs},
AUTHOR = {Hariharan, Ramesh and Telikepalli, Kavitha and Mehlhorn, Kurt},
EDITOR = {Bugliesi, Michele and Preneel, Bart and Sassone, Vladimir and Wegener, Ingo},
LANGUAGE = {eng},
ISBN = {3-540-35904-4},
LOCALID = {Local-ID: C1256428004B93B8-C5345CC3A9361E5BC12571CA003B984B-HTM06a},
PUBLISHER = {Springer},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {--1,0,1} edge incidence vector is associated with each cycle: edges traversed by the cycle in the right direction get 1 and edges traversed in the opposite direction get -1. The vector space over generated by these vectors is the cycle space of G. A minimum cycle basis is a set of cycles of minimum weight that span the cycle space of G. The current fastest algorithm for computing a minimum cycle basis in a directed graph with m edges and n vertices runs in time (where $\omega$< 2.376 is the exponent of matrix multiplication). Here we present an O(m3n + m2n2logn) algorithm. We also slightly improve the running time of the current fastest randomized algorithm from O(m2nlogn) to O(m2 n + mn2 logn).},
BOOKTITLE = {Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I},
PAGES = {250--261},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4051},
}

Endnote

%0 Conference Proceedings
%A Hariharan, Ramesh
%A Telikepalli, Kavitha
%A Mehlhorn, Kurt
%E Bugliesi, Michele
%E Preneel, Bart
%E Sassone, Vladimir
%E Wegener, Ingo
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-21DE-7
%F EDOC: 314560
%F OTHER: Local-ID: C1256428004B93B8-C5345CC3A9361E5BC12571CA003B984B-HTM06a
%D 2006
%B Untitled Event
%Z date of event: 2006-07-10 -
%C Venice, Italy
%X We consider the problem of computing a minimum cycle basis in a directed graph.
The input to this problem is a directed graph G whose edges have non-negative
weights. A cycle in this graph is actually a cycle in the underlying undirected
graph with edges traversable in both directions. A {–1,0,1} edge incidence
vector is associated with each cycle: edges traversed by the cycle in the right
direction get 1 and edges traversed in the opposite direction get -1. The
vector space over generated by these vectors is the cycle space of G. A minimum
cycle basis is a set of cycles of minimum weight that span the cycle space of
G. The current fastest algorithm for computing a minimum cycle basis in a
directed graph with m edges and n vertices runs in time (where ω< 2.376 is the
exponent of matrix multiplication). Here we present an O(m3n + m2n2logn)
algorithm. We also slightly improve the running time of the current fastest
randomized algorithm from O(m2nlogn) to O(m2 n + mn2 logn).
%B Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I
%P 250 - 261
%I Springer
%@ 3-540-35904-4
%B Lecture Notes in Computer Science
%N 4051

[179]

R. W. Irving, T. Kavitha, K. Mehlhorn, D. Michail, and K. Paluch, “Rank-Maximal Matchings,” ACM Transactions on Algorithms, vol. 2, 2006.

Abstract

Suppose that each member of a set A of applicants ranks a subset of a set P of
posts in an order of preference, possibly involving ties. A matching is a set
of (applicant, post) pairs such that each applicant and each post appears in at
most one pair. A rank-maximal matching is one in which the maximum possible
number of applicants are matched to their first choice post, and subject to
that condition, the maximum possible number are matched to their second choice
post, and so on. This is a relevant concept in any practical matching situation
and it was first studied by Irving [2003].We give an algorithm to compute a
rank-maximal matching with running time O(min(n + C,C√n)m), where C is the
maximal rank of an edge used in a rank-maximal matching, n is the number of
applicants and posts and m is the total size of the preference lists.

Export

BibTeX

@article{ITMMP2006,
TITLE = {Rank-Maximal Matchings},
AUTHOR = {Irving, Robert W. and Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios and Paluch, Katarzyna},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-B6D1D2487C87162EC125728E003DA65E-ITMMP2006},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {Suppose that each member of a set A of applicants ranks a subset of a set P of posts in an order of preference, possibly involving ties. A matching is a set of (applicant, post) pairs such that each applicant and each post appears in at most one pair. A rank-maximal matching is one in which the maximum possible number of applicants are matched to their first choice post, and subject to that condition, the maximum possible number are matched to their second choice post, and so on. This is a relevant concept in any practical matching situation and it was first studied by Irving [2003].We give an algorithm to compute a rank-maximal matching with running time O(min(n + C,C$\surd$n)m), where C is the maximal rank of an edge used in a rank-maximal matching, n is the number of applicants and posts and m is the total size of the preference lists.},
JOURNAL = {ACM Transactions on Algorithms},
VOLUME = {2},
PAGES = {602--610},
}

Endnote

%0 Journal Article
%A Irving, Robert W.
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Paluch, Katarzyna
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Rank-Maximal Matchings :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-23C5-9
%F EDOC: 314364
%F OTHER: Local-ID: C1256428004B93B8-B6D1D2487C87162EC125728E003DA65E-ITMMP2006
%D 2006
%* Review method: peer-reviewed
%X Suppose that each member of a set A of applicants ranks a subset of a set P of
posts in an order of preference, possibly involving ties. A matching is a set
of (applicant, post) pairs such that each applicant and each post appears in at
most one pair. A rank-maximal matching is one in which the maximum possible
number of applicants are matched to their first choice post, and subject to
that condition, the maximum possible number are matched to their second choice
post, and so on. This is a relevant concept in any practical matching situation
and it was first studied by Irving [2003].We give an algorithm to compute a
rank-maximal matching with running time O(min(n + C,C√n)m), where C is the
maximal rank of an edge used in a rank-maximal matching, n is the number of
applicants and posts and m is the total size of the preference lists.
%J ACM Transactions on Algorithms
%V 2
%& 602
%P 602 - 610

[180]

L. Kettner, K. Mehlhorn, S. Pion, S. Schirra, and C. Yap, “Reply to ‘Backward Error Analysis ...,’” in Computational Science and Its Applications - ICCSA 2006, I, 2006.

Abstract

The algorithms of computational geometry are designed for a machine model with
exact real arithmetic. Substituting floating-point arithmetic for the assumed
real arithmetic may cause implementations to fail. Although this is well known,
it is not common knowledge. There is no paper that systematically discusses
what can go wrong and provides simple examples for the di.erent ways in which
floating-point implementations can fail. Due to this lack of examples,
instructors of computational geometry have little material for demonstrating
the inadequacy of floating-point arithmetic for geometric computations,
students of computational geometry and implementers of geometric algorithms
still underestimate the seriousness of the problem, and researchers in our and
neighboring disciplines still believe that simple approaches are able to
overcome the problem. In this paper, we study simple algorithms for two simple
geometric problems, namely computing convex hulls and triangulations of point
sets, and show how they can fail and explain why they fail when executed with
floating-point arithmetic.

Export

BibTeX

@inproceedings{mehlhorn06,
TITLE = {Reply to "Backward Error Analysis ..."},
AUTHOR = {Kettner, Lutz and Mehlhorn, Kurt and Pion, Sylvain and Schirra, Stefan and Yap, Chee},
EDITOR = {Gavrilova, Marina and Gervasi, Osvaldo and Kumar, Vipin and Tan, C. J.Kenneth and Taniar, David and Lagan{\`a}, Antonio and Mun, Youngsong and Choo, Hyunseung},
LANGUAGE = {eng},
ISBN = {3-540-34070-X},
LOCALID = {Local-ID: C1256428004B93B8-47155FF99A36D907C12571F1002C58B0-mehlhorn06},
PUBLISHER = {Springer},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {The algorithms of computational geometry are designed for a machine model with exact real arithmetic. Substituting floating-point arithmetic for the assumed real arithmetic may cause implementations to fail. Although this is well known, it is not common knowledge. There is no paper that systematically discusses what can go wrong and provides simple examples for the di.erent ways in which floating-point implementations can fail. Due to this lack of examples, instructors of computational geometry have little material for demonstrating the inadequacy of floating-point arithmetic for geometric computations, students of computational geometry and implementers of geometric algorithms still underestimate the seriousness of the problem, and researchers in our and neighboring disciplines still believe that simple approaches are able to overcome the problem. In this paper, we study simple algorithms for two simple geometric problems, namely computing convex hulls and triangulations of point sets, and show how they can fail and explain why they fail when executed with floating-point arithmetic.},
BOOKTITLE = {Computational Science and Its Applications -- ICCSA 2006, I},
PAGES = {60--60},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3980},
}

Endnote

%0 Conference Proceedings
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Pion, Sylvain
%A Schirra, Stefan
%A Yap, Chee
%E Gavrilova, Marina
%E Gervasi, Osvaldo
%E Kumar, Vipin
%E Tan, C. J.Kenneth
%E Taniar, David
%E Laganà, Antonio
%E Mun, Youngsong
%E Choo, Hyunseung
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Reply to "Backward Error Analysis ..." :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-23DB-8
%F EDOC: 314401
%F OTHER: Local-ID: C1256428004B93B8-47155FF99A36D907C12571F1002C58B0-mehlhorn06
%D 2006
%B Untitled Event
%Z date of event: 2006-05-08 -
%C Glasgow, UK
%X The algorithms of computational geometry are designed for a machine model with
exact real arithmetic. Substituting floating-point arithmetic for the assumed
real arithmetic may cause implementations to fail. Although this is well known,
it is not common knowledge. There is no paper that systematically discusses
what can go wrong and provides simple examples for the di.erent ways in which
floating-point implementations can fail. Due to this lack of examples,
instructors of computational geometry have little material for demonstrating
the inadequacy of floating-point arithmetic for geometric computations,
students of computational geometry and implementers of geometric algorithms
still underestimate the seriousness of the problem, and researchers in our and
neighboring disciplines still believe that simple approaches are able to
overcome the problem. In this paper, we study simple algorithms for two simple
geometric problems, namely computing convex hulls and triangulations of point
sets, and show how they can fail and explain why they fail when executed with
floating-point arithmetic.
%B Computational Science and Its Applications - ICCSA 2006, I
%P 60 - 60
%I Springer
%@ 3-540-34070-X
%B Lecture Notes in Computer Science
%N 3980

[181]

W. Krandick and K. Mehlhorn, “New bounds for the Descartes method,” Journal of Symbolic Computation, vol. 41, no. 1, 2006.

Abstract

We give a new bound for the number of recursive subdivisions in the Descartes <br>method for polynomial real root isolation. Our proof uses Ostrowski’s theory of <br>normal power series from 1950 which has so far been overlooked in the <br>literature. We combine Ostrowski’s results with a theorem of Davenport from <br>1985 to obtain our bound. We also characterize normality of cubic polynomials <br>by explicit conditions on their roots and derive a generalization of one of <br>Ostrowski’s theorems.

Export

BibTeX

@article{Krandick2006JSC,
TITLE = {New bounds for the {D}escartes method},
AUTHOR = {Krandick, Werner and Mehlhorn, Kurt},
LANGUAGE = {eng},
DOI = {10.1016/j.jsc.2005.02.004},
LOCALID = {Local-ID: C1256428004B93B8-8291BD2AF8984049C12571C50041D379-mehlhorn06e},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {We give a new bound for the number of recursive subdivisions in the Descartes <br>method for polynomial real root isolation. Our proof uses Ostrowski{\textquoteright}s theory of <br>normal power series from 1950 which has so far been overlooked in the <br>literature. We combine Ostrowski{\textquoteright}s results with a theorem of Davenport from <br>1985 to obtain our bound. We also characterize normality of cubic polynomials <br>by explicit conditions on their roots and derive a generalization of one of <br>Ostrowski{\textquoteright}s theorems.},
JOURNAL = {Journal of Symbolic Computation},
VOLUME = {41},
NUMBER = {1},
PAGES = {49--66},
}

Endnote

%0 Journal Article
%A Krandick, Werner
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New bounds for the Descartes method :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2384-C
%F EDOC: 314367
%F OTHER: Local-ID: C1256428004B93B8-8291BD2AF8984049C12571C50041D379-mehlhorn06e
%R 10.1016/j.jsc.2005.02.004
%D 2006
%* Review method: peer-reviewed
%X We give a new bound for the number of recursive subdivisions in the Descartes <br>method for polynomial real root isolation. Our proof uses Ostrowski’s theory of <br>normal power series from 1950 which has so far been overlooked in the <br>literature. We combine Ostrowski’s results with a theorem of Davenport from <br>1985 to obtain our bound. We also characterize normality of cubic polynomials <br>by explicit conditions on their roots and derive a generalization of one of <br>Ostrowski’s theorems.
%J Journal of Symbolic Computation
%V 41
%N 1
%& 49
%P 49 - 66

[182]

D. Kratsch, R. McConnell, K. Mehlhorn, and J. P. Spinrad, “Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs,” SIAM Journal on Computing, vol. 36, 2006.

Abstract

A certifying algorithm for a problem is an algorithm that provides a
certificate with each answer that it produces. The certificate is a piece of
evidence that proves that the answer has not been compromised by a bug in the
implementation. We give linear-time certifying algorithms for recognition of
interval graphs and permutation graphs, and for a few other related problems.
Previous algorithms fail to provide supporting evidence when they claim that
the input graph is not a member of the class. We show that our certificates of
nonmembership can be authenticated in O(|V|) time.

Export

BibTeX

@article{mehlhorn06b,
TITLE = {Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs},
AUTHOR = {Kratsch, Dieter and McConnell, Ross and Mehlhorn, Kurt and Spinrad, Jeremy P.},
LANGUAGE = {eng},
ISSN = {0097-5397},
LOCALID = {Local-ID: C1256428004B93B8-90DAACD3D4A0C6A8C1256E20004505E1-mehlhorn06b},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been compromised by a bug in the implementation. We give linear-time certifying algorithms for recognition of interval graphs and permutation graphs, and for a few other related problems. Previous algorithms fail to provide supporting evidence when they claim that the input graph is not a member of the class. We show that our certificates of nonmembership can be authenticated in O(|V|) time.},
JOURNAL = {SIAM Journal on Computing},
VOLUME = {36},
PAGES = {326--353},
}

Endnote

%0 Journal Article
%A Kratsch, Dieter
%A McConnell, Ross
%A Mehlhorn, Kurt
%A Spinrad, Jeremy P.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-224D-0
%F EDOC: 314649
%F OTHER: Local-ID: C1256428004B93B8-90DAACD3D4A0C6A8C1256E20004505E1-mehlhorn06b
%D 2006
%* Review method: peer-reviewed
%X A certifying algorithm for a problem is an algorithm that provides a
certificate with each answer that it produces. The certificate is a piece of
evidence that proves that the answer has not been compromised by a bug in the
implementation. We give linear-time certifying algorithms for recognition of
interval graphs and permutation graphs, and for a few other related problems.
Previous algorithms fail to provide supporting evidence when they claim that
the input graph is not a member of the class. We show that our certificates of
nonmembership can be authenticated in O(|V|) time.
%J SIAM Journal on Computing
%V 36
%& 326
%P 326 - 353
%@ false

[183]

K. Mehlhorn, R. Osbild, and M. Sagraloff, “Reliable and Efficient Computational Geometry Via Controlled Perturbation,” in Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I, 2006.

Abstract

Most algorithms of computational geometry are designed for the Real-RAM and
non-degenerate input. We call such algorithms idealistic. Executing an
idealistic algorithm with floating point arithmetic may fail. Controlled
perturbation replaces an input x by a random nearby in the δ-neighborhood of x
and then runs the floating point version of the idealistic algorithm on . The
hope is that this will produce the correct result for with constant probability
provided that δ is small and the precision L of the floating point system is
large enough. We turn this hope into a theorem for a large class of geometric
algorithms and describe a general methodology for deriving a relation between δ
and L. We exemplify the usefulness of the methodology by examples.
Partially supported by the IST Programme of the EU under Contract No
IST-006413, Algorithms for Complex Shapes (ACS).

Export

BibTeX

@inproceedings{MOS06,
TITLE = {Reliable and Efficient Computational Geometry Via Controlled Perturbation},
AUTHOR = {Mehlhorn, Kurt and Osbild, Ralf and Sagraloff, Michael},
EDITOR = {Bugliesi, Michele and Preneel, Bart and Sassone, Vladimir and Wegener, Ingo},
LANGUAGE = {eng},
ISBN = {3-540-35904-4},
LOCALID = {Local-ID: C1256428004B93B8-1C44F76383A124E7C12571CA003ABB0D-MOS06},
PUBLISHER = {Springer},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {Most algorithms of computational geometry are designed for the Real-RAM and non-degenerate input. We call such algorithms idealistic. Executing an idealistic algorithm with floating point arithmetic may fail. Controlled perturbation replaces an input x by a random nearby in the $\delta$-neighborhood of x and then runs the floating point version of the idealistic algorithm on . The hope is that this will produce the correct result for with constant probability provided that $\delta$ is small and the precision L of the floating point system is large enough. We turn this hope into a theorem for a large class of geometric algorithms and describe a general methodology for deriving a relation between $\delta$ and L. We exemplify the usefulness of the methodology by examples. Partially supported by the IST Programme of the EU under Contract No IST-006413, Algorithms for Complex Shapes (ACS).},
BOOKTITLE = {Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I},
PAGES = {299--310},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {4051},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Osbild, Ralf
%A Sagraloff, Michael
%E Bugliesi, Michele
%E Preneel, Bart
%E Sassone, Vladimir
%E Wegener, Ingo
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Reliable and Efficient Computational Geometry Via Controlled Perturbation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-23D5-3
%F EDOC: 314533
%F OTHER: Local-ID: C1256428004B93B8-1C44F76383A124E7C12571CA003ABB0D-MOS06
%D 2006
%B Untitled Event
%Z date of event: 2006-07-10 -
%C Venice, Italy
%X Most algorithms of computational geometry are designed for the Real-RAM and
non-degenerate input. We call such algorithms idealistic. Executing an
idealistic algorithm with floating point arithmetic may fail. Controlled
perturbation replaces an input x by a random nearby in the δ-neighborhood of x
and then runs the floating point version of the idealistic algorithm on . The
hope is that this will produce the correct result for with constant probability
provided that δ is small and the precision L of the floating point system is
large enough. We turn this hope into a theorem for a large class of geometric
algorithms and describe a general methodology for deriving a relation between δ
and L. We exemplify the usefulness of the methodology by examples.
Partially supported by the IST Programme of the EU under Contract No
IST-006413, Algorithms for Complex Shapes (ACS).
%B Automata, Languages and Programming, 33rd International Colloquium, ICALP 2006, Part I
%P 299 - 310
%I Springer
%@ 3-540-35904-4
%B Lecture Notes in Computer Science
%N 4051

[184]

K. Mehlhorn, “Reliable and Efficient Geometric Computing,” in Algorithms and Complexity : 6th Italian Conference, CIAC 2006, 2006.

Abstract

Reliable implementation of geometric algorithms is a notoriously difficult
task. Algorithms are usually designed for the Real-RAM, capable of computing
with real numbers in the sense of mathematics, and for non-degenerate inputs.
But, real computers are not Real-RAMs and inputs are frequently degenerate.
In the first part of the talk we illustrate the pitfalls of geometric computing
by way of examples [KMP+04]. The examples demonstrate in a lucid way that
standard and frequently taught algorithms can go completely astray when naively
implemented with floating point arithmetic.
Partially supported by the IST Programme of the EU under Contract No
IST-2005-TODO, Algorithms for Complex Shapes (ACS).

Export

BibTeX

@inproceedings{mehlhorn06x,
TITLE = {Reliable and Efficient Geometric Computing},
AUTHOR = {Mehlhorn, Kurt},
EDITOR = {Calamoneri, Tiziana and Finocchi, Irene and Italiano, Giuseppe F.},
LANGUAGE = {eng},
ISBN = {3-540-34375-X},
LOCALID = {Local-ID: C1256428004B93B8-EC5B8ABF87E0F995C12571F1002BEFEC-mehlhorn06x},
PUBLISHER = {Springer},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {Reliable implementation of geometric algorithms is a notoriously difficult task. Algorithms are usually designed for the Real-RAM, capable of computing with real numbers in the sense of mathematics, and for non-degenerate inputs. But, real computers are not Real-RAMs and inputs are frequently degenerate. In the first part of the talk we illustrate the pitfalls of geometric computing by way of examples [KMP+04]. The examples demonstrate in a lucid way that standard and frequently taught algorithms can go completely astray when naively implemented with floating point arithmetic. Partially supported by the IST Programme of the EU under Contract No IST-2005-TODO, Algorithms for Complex Shapes (ACS).},
BOOKTITLE = {Algorithms and Complexity : 6th Italian Conference, CIAC 2006},
PAGES = {1--2},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3998},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%E Calamoneri, Tiziana
%E Finocchi, Irene
%E Italiano, Giuseppe F.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Reliable and Efficient Geometric Computing :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-23D8-E
%F EDOC: 314562
%F OTHER: Local-ID: C1256428004B93B8-EC5B8ABF87E0F995C12571F1002BEFEC-mehlhorn06x
%D 2006
%B Untitled Event
%Z date of event: 2006-05-29 -
%C Rome, Italy
%X Reliable implementation of geometric algorithms is a notoriously difficult
task. Algorithms are usually designed for the Real-RAM, capable of computing
with real numbers in the sense of mathematics, and for non-degenerate inputs.
But, real computers are not Real-RAMs and inputs are frequently degenerate.
In the first part of the talk we illustrate the pitfalls of geometric computing
by way of examples [KMP+04]. The examples demonstrate in a lucid way that
standard and frequently taught algorithms can go completely astray when naively
implemented with floating point arithmetic.
Partially supported by the IST Programme of the EU under Contract No
IST-2005-TODO, Algorithms for Complex Shapes (ACS).
%B Algorithms and Complexity : 6th Italian Conference, CIAC 2006
%P 1 - 2
%I Springer
%@ 3-540-34375-X
%B Lecture Notes in Computer Science
%N 3998

[185]

K. Mehlhorn and D. Michail, “Implementing Minimum Cycle Basis Algorithms,” ACM Journal of Experimental Algorithmics, vol. 11, 2006.

Abstract

In this paper, we consider the problem of computing a minimum cycle basis of an
undirected graph G = (V,E) with n vertices and m edges. We describe an
efficient implementation of an O(m3 + mn2 log n) algorithm. For sparse
graphs, this is the currently best-known algorithm. This algorithm's running
time can be partitioned into two parts with time O(m3) and O(m2n + mn2 log
n), respectively. Our experimental findings imply that for random graphs the
true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log
n) part. A straightforward implementation would require Ω(nm) shortest-path
computations. Thus, we develop several heuristics in order to get a practical
algorithm. Our experiments show that in random graphs our techniques result in
a significant speed-up. Based on our experimental observations, we combine the
two fundamentally different approaches to compute a minimum cycle basis to
obtain a new hybrid algorithm with running time O(m2n2). The hybrid algorithm
is very efficient, in practice, for random dense unweighted graphs. Finally, we
compare these two algorithms with a number of previous implementations for
finding a minimum cycle basis of an undirected graph.

Export

BibTeX

@article{MM06,
TITLE = {Implementing Minimum Cycle Basis Algorithms},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-6975DD6D0B820206C125728E003E04A2-MM06},
YEAR = {2006},
DATE = {2006},
ABSTRACT = {In this paper, we consider the problem of computing a minimum cycle basis of an undirected graph G = (V,E) with n vertices and m edges. We describe an efficient implementation of an O(m3 + mn2 log n) algorithm. For sparse graphs, this is the currently best-known algorithm. This algorithm's running time can be partitioned into two parts with time O(m3) and O(m2n + mn2 log n), respectively. Our experimental findings imply that for random graphs the true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log n) part. A straightforward implementation would require $\Omega$(nm) shortest-path computations. Thus, we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speed-up. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis to obtain a new hybrid algorithm with running time O(m2n2). The hybrid algorithm is very efficient, in practice, for random dense unweighted graphs. Finally, we compare these two algorithms with a number of previous implementations for finding a minimum cycle basis of an undirected graph.},
JOURNAL = {ACM Journal of Experimental Algorithmics},
VOLUME = {11},
PAGES = {1--14},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Implementing Minimum Cycle Basis Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2320-A
%F EDOC: 314579
%F OTHER: Local-ID: C1256428004B93B8-6975DD6D0B820206C125728E003E04A2-MM06
%D 2006
%X In this paper, we consider the problem of computing a minimum cycle basis of an
undirected graph G = (V,E) with n vertices and m edges. We describe an
efficient implementation of an O(m3 + mn2 log n) algorithm. For sparse
graphs, this is the currently best-known algorithm. This algorithm's running
time can be partitioned into two parts with time O(m3) and O(m2n + mn2 log
n), respectively. Our experimental findings imply that for random graphs the
true bottleneck of a sophisticated implementation is the O(m2 n + mn2 log
n) part. A straightforward implementation would require Ω(nm) shortest-path
computations. Thus, we develop several heuristics in order to get a practical
algorithm. Our experiments show that in random graphs our techniques result in
a significant speed-up. Based on our experimental observations, we combine the
two fundamentally different approaches to compute a minimum cycle basis to
obtain a new hybrid algorithm with running time O(m2n2). The hybrid algorithm
is very efficient, in practice, for random dense unweighted graphs. Finally, we
compare these two algorithms with a number of previous implementations for
finding a minimum cycle basis of an undirected graph.
%J ACM Journal of Experimental Algorithmics
%V 11
%& 1
%P 1 - 14

2005

[186]

D. Abraham, R. Irving, K. Mehlhorn, and T. Kavitha, “Popular Matchings,” in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, Canada, 2005.

Export

BibTeX

@inproceedings{AIKM05,
TITLE = {Popular Matchings},
AUTHOR = {Abraham, David and Irving, Robert and Mehlhorn, Kurt and Kavitha, Telikepalli},
LANGUAGE = {eng},
ISBN = {0-89871-585-7},
PUBLISHER = {SIAM},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005)},
PAGES = {424--432},
ADDRESS = {Vancouver, Canada},
}

Endnote

%0 Conference Proceedings
%A Abraham, David
%A Irving, Robert
%A Mehlhorn, Kurt
%A Kavitha, Telikepalli
%+ External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Popular Matchings :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2765-0
%F EDOC: 279204
%D 2005
%B Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2005-01-23 - 2005-01-25
%C Vancouver, Canada
%B Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%P 424 - 432
%I SIAM
%@ 0-89871-585-7

[187]

D. Abraham, K. Cechlárová, D. F. Manlove, and K. Mehlhorn, “Pareto Optimality in House Allocation Problems,” in Algorithms and Computation (ISAAC 2004), Hong Kong, China, 2005.

Export

BibTeX

@inproceedings{ACMM04,
TITLE = {Pareto Optimality in House Allocation Problems},
AUTHOR = {Abraham, David and Cechl{\'a}rov{\'a}, Katarina and Manlove, David F. and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-24131-0},
DOI = {10.1007/978-3-540-30551-4_3},
PUBLISHER = {Springer},
YEAR = {2004},
DATE = {2005},
BOOKTITLE = {Algorithms and Computation (ISAAC 2004)},
EDITOR = {Fleischer, Rudolf and Trippen, G.},
PAGES = {3--15},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3341},
ADDRESS = {Hong Kong, China},
}

Endnote

%0 Conference Proceedings
%A Abraham, David
%A Cechlárová, Katarina
%A Manlove, David F.
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Pareto Optimality in House Allocation Problems :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-E36F-9
%R 10.1007/978-3-540-30551-4_3
%D 2005
%B 15th International Symposium on Algorithms and Computation
%Z date of event: 2004-12-20 - 2004-12-22
%C Hong Kong, China
%B Algorithms and Computation
%E Fleischer, Rudolf; Trippen, G.
%P 3 - 15
%I Springer
%@ 3-540-24131-0
%B Lecture Notes in Computer Science
%N 3341

[188]

D. J. Abraham, K. Cechlárová, D. Manlove, and K. Mehlhorn, “Pareto Optimality in House Allocation Problems,” in Algorithms and computation (ISAAC 2005), Sanya, Hainan, China, 2005.

Export

BibTeX

@inproceedings{mehlhorn06y,
TITLE = {Pareto Optimality in House Allocation Problems},
AUTHOR = {Abraham, David J. and Cechl{\'a}rov{\'a}, Katar{\'i}na and Manlove, David and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-30935-7},
DOI = {10.1007/11602613_115},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {Algorithms and computation (ISAAC 2005)},
EDITOR = {Deng, Xiaotie and Du, Dingzhu},
PAGES = {1163--1175},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3827},
ADDRESS = {Sanya, Hainan, China},
}

Endnote

%0 Conference Proceedings
%A Abraham, David J.
%A Cechlárová, Katarína
%A Manlove, David
%A Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Pareto Optimality in House Allocation Problems :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-E369-6
%R 10.1007/11602613_115
%D 2005
%B ISAAC 2005
%Z date of event: 2005-12-19 - 2005-12-21
%C Sanya, Hainan, China
%B Algorithms and computation
%E Deng, Xiaotie; Du, Dingzhu
%P 1163 - 1175
%I Springer
%@ 3-540-30935-7
%B Lecture Notes in Computer Science
%N 3827

[189]

S. Baswana, T. Kavitha, K. Mehlhorn, and S. Pettie, “New Constructions of (alpha, beta)-Spanners and Purely Additive Spanners,” in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, Canada, 2005.

Export

BibTeX

@inproceedings{BaswanaEtal2005,
TITLE = {New Constructions of (alpha, beta)-Spanners and Purely Additive Spanners},
AUTHOR = {Baswana, Surender and Kavitha, Telikepalli and Mehlhorn, Kurt and Pettie, Seth},
LANGUAGE = {eng},
ISBN = {0-89871-585-7},
PUBLISHER = {SIAM},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005)},
PAGES = {672--681},
ADDRESS = {Vancouver, Canada},
}

Endnote

%0 Conference Proceedings
%A Baswana, Surender
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Pettie, Seth
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New Constructions of (alpha, beta)-Spanners and Purely Additive Spanners :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2726-F
%F EDOC: 279195
%D 2005
%B Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2005-01-23 - 2005-01-26
%C Vancouver, Canada
%B Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%P 672 - 681
%I SIAM
%@ 0-89871-585-7

[190]

E. Berberich, A. Eigenwillig, M. Hemmer, S. Hert, L. Kettner, K. Mehlhorn, J. Reichel, S. Schmitt, E. Schömer, and N. Wolpert, “EXACUS: Efficient and Exact Algorithms for Curves and Surfaces,” in Algorithms -- ESA 2005, Palma de Mallorca, Spain, 2005.

Abstract

We present the first open-source release of the
C\texttt{++} libraries of the \textsc{Exacus} project
of the Max-Planck-Institut f{\"u}r Informatik. Our
software computes arrangements of curves and curve
segments, and boolean operations on polygons bounded
by curve segments. We pursued the goals efficiency,
correctness, and completeness for all input cases,
implying robustness. We present the structure of the
libraries and their generic design. With our work we
contribute one milestone on the way towards a
systematic support of non-linear geometry in software
libraries.

Export

BibTeX

@inproceedings{Berberich05,
TITLE = {{EXACUS}: Efficient and Exact Algorithms for Curves and Surfaces},
AUTHOR = {Berberich, Eric and Eigenwillig, Arno and Hemmer, Michael and Hert, Susan and Kettner, Lutz and Mehlhorn, Kurt and Reichel, Joachim and Schmitt, Susanne and Sch{\"o}mer, Elmar and Wolpert, Nicola},
LANGUAGE = {eng},
ISBN = {3-540-29118-0},
DOI = {10.1007/11561071_16},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
ABSTRACT = {We present the first open-source release of the C\texttt{++} libraries of the \textsc{Exacus} project of the Max-Planck-Institut f{\"u}r Informatik. Our software computes arrangements of curves and curve segments, and boolean operations on polygons bounded by curve segments. We pursued the goals efficiency, correctness, and completeness for all input cases, implying robustness. We present the structure of the libraries and their generic design. With our work we contribute one milestone on the way towards a systematic support of non-linear geometry in software libraries.},
BOOKTITLE = {Algorithms -- ESA 2005},
EDITOR = {St{\o}lting Brodal, Gerth and Leonardi, Stefano},
PAGES = {155--166},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3669},
ADDRESS = {Palma de Mallorca, Spain},
}

Endnote

%0 Conference Proceedings
%A Berberich, Eric
%A Eigenwillig, Arno
%A Hemmer, Michael
%A Hert, Susan
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Reichel, Joachim
%A Schmitt, Susanne
%A Schömer, Elmar
%A Wolpert, Nicola
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T EXACUS: Efficient and Exact Algorithms for Curves and Surfaces :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2677-0
%F EDOC: 279189
%R 10.1007/11561071_16
%D 2005
%B 13th Annual European Symposium on Algorithms
%Z date of event: 2005-10-03 - 2005-10-06
%C Palma de Mallorca, Spain
%X We present the first open-source release of the
C\texttt{++} libraries of the \textsc{Exacus} project
of the Max-Planck-Institut f{\"u}r Informatik. Our
software computes arrangements of curves and curve
segments, and boolean operations on polygons bounded
by curve segments. We pursued the goals efficiency,
correctness, and completeness for all input cases,
implying robustness. We present the structure of the
libraries and their generic design. With our work we
contribute one milestone on the way towards a
systematic support of non-linear geometry in software
libraries.
%B Algorithms -- ESA 2005
%E Stølting Brodal, Gerth; Leonardi, Stefano
%P 155 - 166
%I Springer
%@ 3-540-29118-0
%B Lecture Notes in Computer Science
%N 3669

[191]

A. Eigenwillig, L. Kettner, W. Krandick, K. Mehlhorn, S. Schmitt, and N. Wolpert, “A Descartes Algorithm for Polynomials with Bit-Stream Coefficients,” in Computer Algebra in Scientific Computing (CASC 2005), Kalamata, Greece, 2005.

Export

BibTeX

@inproceedings{Eigenwillig2005,
TITLE = {A {D}escartes Algorithm for Polynomials with Bit-Stream Coefficients},
AUTHOR = {Eigenwillig, Arno and Kettner, Lutz and Krandick, Werner and Mehlhorn, Kurt and Schmitt, Susanne and Wolpert, Nicola},
LANGUAGE = {eng},
ISBN = {3-540-28966-6},
DOI = {10.1007/11555964_12},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {Computer Algebra in Scientific Computing (CASC 2005)},
EDITOR = {Ganzha, Victor G. and Mayr, Ernst W. and Vorozhtsov, Evgenii V.},
PAGES = {138--149},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3718},
ADDRESS = {Kalamata, Greece},
}

Endnote

%0 Conference Proceedings
%A Eigenwillig, Arno
%A Kettner, Lutz
%A Krandick, Werner
%A Mehlhorn, Kurt
%A Schmitt, Susanne
%A Wolpert, Nicola
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Descartes Algorithm for Polynomials with Bit-Stream Coefficients :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2589-1
%F EDOC: 279177
%R 10.1007/11555964_12
%D 2005
%B The 8th International Workshop on Computer Algebra in Scientific Computing
%Z date of event: 2005-09-12 -
%C Kalamata, Greece
%B Computer Algebra in Scientific Computing
%E Ganzha, Victor G.; Mayr, Ernst W.; Vorozhtsov, Evgenii V.
%P 138 - 149
%I Springer
%@ 3-540-28966-6
%B Lecture Notes in Computer Science
%N 3718

[192]

S. Funke, K. Mehlhorn, and S. Näher, “Structural Filtering: a Paradigm for Efficient and Exact Geometric Programs,” Computational Geometry, vol. 31, no. 3, 2005.

Export

BibTeX

@article{mehlhorn05z,
TITLE = {Structural Filtering: a Paradigm for Efficient and Exact Geometric Programs},
AUTHOR = {Funke, Stefan and Mehlhorn, Kurt and N{\"a}her, Stefan},
LANGUAGE = {eng},
DOI = {10.1016/j.comgeo.2004.12.007},
YEAR = {2005},
DATE = {2005},
JOURNAL = {Computational Geometry},
VOLUME = {31},
NUMBER = {3},
PAGES = {179--194},
}

Endnote

%0 Journal Article
%A Funke, Stefan
%A Mehlhorn, Kurt
%A Näher, Stefan
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Structural Filtering: a Paradigm for Efficient and Exact Geometric Programs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-E9E4-B
%R 10.1016/j.comgeo.2004.12.007
%D 2005
%J Computational Geometry
%V 31
%N 3
%& 179
%P 179 - 194

[193]

S. Funke, C. Klein, K. Mehlhorn, and S. Schmitt, “Controlled Perturbation for Delaunay Triangulations,” in Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005), Vancouver, Canada, 2005.

Abstract

Most geometric algorithms are idealistic in the sense that they are designed
for the Real-RAM model of computation and for inputs in general
position. Real inputs may be degenerate and floating point arithmetic is
only an approximation of real arithmetic.
Perturbation replaces an input by a nearby input which is (hopefully)
in general position and on which the algorithm can be run with floating point
arithmetic. Controlled perturbation as proposed by Halperin et al. calls for
more: control over the amount of perturbation needed for a given precision of
the floating point system. Or conversely, a control over the precision needed
for a given amount of perturbation. Halperin et al.~gave controlled
perturbation schemes for arrangements of polyhedral surfaces, spheres, and
circles. We extend their work and point out that controlled perturbation is a
general scheme for converting idealistic algorithms into algorithms which can
be executed with floating point arithmetic. We also show how to use controlled
perturbation in the context of randomized geometric algorithms without
deteriorating the running time. Finally, we give concrete schemes for planar
Delaunay triangulations and convex hulls and Delaunay triangulations in
arbitrary dimensions. We analyze the relation between the
perturbation amount and the precision of the floating point system. We also
report about experiments with a planar Delaunay diagram algorithm.

Export

BibTeX

@inproceedings{FKMS2005,
TITLE = {Controlled Perturbation for {Delaunay} Triangulations},
AUTHOR = {Funke, Stefan and Klein, Christian and Mehlhorn, Kurt and Schmitt, Susanne},
LANGUAGE = {eng},
ISBN = {0-89871-585-7},
URL = {http://dl.acm.org/citation.cfm?id=1070432.1070582},
LOCALID = {Local-ID: C1256428004B93B8-51E79341608E6746C1256FA2005B7772-FKMS2005},
PUBLISHER = {SIAM},
YEAR = {2005},
DATE = {2005},
ABSTRACT = {Most geometric algorithms are idealistic in the sense that they are designed for the Real-RAM model of computation and for inputs in general position. Real inputs may be degenerate and floating point arithmetic is only an approximation of real arithmetic. Perturbation replaces an input by a nearby input which is (hopefully) in general position and on which the algorithm can be run with floating point arithmetic. Controlled perturbation as proposed by Halperin et al. calls for more: control over the amount of perturbation needed for a given precision of the floating point system. Or conversely, a control over the precision needed for a given amount of perturbation. Halperin et al.~gave controlled perturbation schemes for arrangements of polyhedral surfaces, spheres, and circles. We extend their work and point out that controlled perturbation is a general scheme for converting idealistic algorithms into algorithms which can be executed with floating point arithmetic. We also show how to use controlled perturbation in the context of randomized geometric algorithms without deteriorating the running time. Finally, we give concrete schemes for planar Delaunay triangulations and convex hulls and Delaunay triangulations in arbitrary dimensions. We analyze the relation between the perturbation amount and the precision of the floating point system. We also report about experiments with a planar Delaunay diagram algorithm.},
BOOKTITLE = {Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2005)},
PAGES = {1047--1056},
ADDRESS = {Vancouver, Canada},
}

Endnote

%0 Conference Proceedings
%A Funke, Stefan
%A Klein, Christian
%A Mehlhorn, Kurt
%A Schmitt, Susanne
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Controlled Perturbation for Delaunay Triangulations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2622-0
%F EDOC: 279162
%F OTHER: Local-ID: C1256428004B93B8-51E79341608E6746C1256FA2005B7772-FKMS2005
%U http://dl.acm.org/citation.cfm?id=1070432.1070582
%D 2005
%B Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2005-01-23 - 2005-01-25
%C Vancouver, Canada
%X Most geometric algorithms are idealistic in the sense that they are designed
for the Real-RAM model of computation and for inputs in general
position. Real inputs may be degenerate and floating point arithmetic is
only an approximation of real arithmetic.
Perturbation replaces an input by a nearby input which is (hopefully)
in general position and on which the algorithm can be run with floating point
arithmetic. Controlled perturbation as proposed by Halperin et al. calls for
more: control over the amount of perturbation needed for a given precision of
the floating point system. Or conversely, a control over the precision needed
for a given amount of perturbation. Halperin et al.~gave controlled
perturbation schemes for arrangements of polyhedral surfaces, spheres, and
circles. We extend their work and point out that controlled perturbation is a
general scheme for converting idealistic algorithms into algorithms which can
be executed with floating point arithmetic. We also show how to use controlled
perturbation in the context of randomized geometric algorithms without
deteriorating the running time. Finally, we give concrete schemes for planar
Delaunay triangulations and convex hulls and Delaunay triangulations in
arbitrary dimensions. We analyze the relation between the
perturbation amount and the precision of the floating point system. We also
report about experiments with a planar Delaunay diagram algorithm.
%B Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%P 1047 - 1056
%I SIAM
%@ 0-89871-585-7

[194]

C. Gotsman, K. Kaligosi, K. Mehlhorn, D. Michail, and E. Pyrga, “Cycle bases of graphs and sampled manifolds,” Max-Planck-Institut für Informatik, Saarbrücken, MPI-I-2005-1-008, 2005.

Abstract

Point samples of a surface in $\R^3$ are the dominant output of a
multitude of 3D scanning devices. The usefulness of these devices rests on
being able to extract properties of the surface from the sample. We show that, under
certain sampling conditions, the minimum cycle basis of a nearest neighbor graph of
the sample encodes topological information about the surface and yields bases for the
trivial and non-trivial loops of the surface. We validate our results by experiments.

Export

BibTeX

@techreport{,
TITLE = {Cycle bases of graphs and sampled manifolds},
AUTHOR = {Gotsman, Craig and Kaligosi, Kanela and Mehlhorn, Kurt and Michail, Dimitrios and Pyrga, Evangelia},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2005-1-008},
NUMBER = {MPI-I-2005-1-008},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {2005},
DATE = {2005},
ABSTRACT = {Point samples of a surface in $\R^3$ are the dominant output of a multitude of 3D scanning devices. The usefulness of these devices rests on being able to extract properties of the surface from the sample. We show that, under certain sampling conditions, the minimum cycle basis of a nearest neighbor graph of the sample encodes topological information about the surface and yields bases for the trivial and non-trivial loops of the surface. We validate our results by experiments.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}

Endnote

%0 Report
%A Gotsman, Craig
%A Kaligosi, Kanela
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Pyrga, Evangelia
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Cycle bases of graphs and sampled manifolds :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0014-684C-E
%U http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2005-1-008
%Y Max-Planck-Institut für Informatik
%C Saarbrücken
%D 2005
%P 30 p.
%X Point samples of a surface in $\R^3$ are the dominant output of a
multitude of 3D scanning devices. The usefulness of these devices rests on
being able to extract properties of the surface from the sample. We show that, under
certain sampling conditions, the minimum cycle basis of a nearest neighbor graph of
the sample encodes topological information about the surface and yields bases for the
trivial and non-trivial loops of the surface. We validate our results by experiments.
%B Research Report / Max-Planck-Institut für Informatik

[195]

K. Kaligosi, K. Mehlhorn, J. I. Munro, and P. Sanders, “Towards Optimal Multiple Selection,” in Automata, Languages and Programming : 32nd International Colloquium, ICALP 2005, 2005.

Export

BibTeX

@inproceedings{mehlhorn05o,
TITLE = {Towards Optimal Multiple Selection},
AUTHOR = {Kaligosi, Kanela and Mehlhorn, Kurt and Munro, J. Ian and Sanders, Peter},
LANGUAGE = {eng},
ISBN = {978-3-540-27580-0},
DOI = {10.1007/11523468_9},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {Automata, Languages and Programming : 32nd International Colloquium, ICALP 2005},
EDITOR = {Caires, Lu{\'i}s and Italiano, Guiseppe F. and Monteiro, Lu{\'i}s and Palamidessi, Catuscia and Yung, Moti},
PAGES = {103--114},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3580},
}

Endnote

%0 Conference Proceedings
%A Kaligosi, Kanela
%A Mehlhorn, Kurt
%A Munro, J. Ian
%A Sanders, Peter
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Towards Optimal Multiple Selection :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-289B-0
%F EDOC: 572236
%R 10.1007/11523468_9
%D 2005
%B Untitled Event
%Z date of event: 2005-07-11 - 2005-07-15
%C Lisboa, Portugal
%B Automata, Languages and Programming : 32nd International Colloquium, ICALP 2005
%E Caires, Luís; Italiano, Guiseppe F.; Monteiro, Luís; Palamidessi, Catuscia; Yung, Moti
%P 103 - 114
%I Springer
%@ 978-3-540-27580-0
%B Lecture Notes in Computer Science
%N 3580

[196]

T. Kavitha and K. Mehlhorn, “A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs,” in STACS 2005, 22nd Annual Symposium on Theoretical Aspects of Computer Science, Stuttgart, Germany, 2005.

Export

BibTeX

@inproceedings{KM2005,
TITLE = {A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-24998-2},
DOI = {10.1007/978-3-540-31856-9_54},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {STACS 2005, 22nd Annual Symposium on Theoretical Aspects of Computer Science},
EDITOR = {Diekert, Volker and Durand, Bruno},
PAGES = {654--665},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3404},
ADDRESS = {Stuttgart, Germany},
}

Endnote

%0 Conference Proceedings
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Polynomial Time Algorithm for Minimum Cycle Basis in Directed Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-25BE-9
%F EDOC: 279158
%R 10.1007/978-3-540-31856-9_54
%D 2005
%B 22nd Annual Symposium on Theoretical Aspects of Computer Science
%Z date of event: 2005-02-24 - 2005-02-26
%C Stuttgart, Germany
%B STACS 2005
%E Diekert, Volker; Durand, Bruno
%P 654 - 665
%I Springer
%@ 3-540-24998-2
%B Lecture Notes in Computer Science
%N 3404

[197]

A. Lars, M. A. Bender, E. Demaine, C. Leiserson, and K. Mehlhorn, Eds., Cache-Oblivious and Cache-Aware Algorithms. Schloss Dagstuhl, 2005.

Export

BibTeX

@proceedings{mehlhornDS05,
TITLE = {Cache-Oblivious and Cache-Aware Algorithms},
EDITOR = {Lars, Arge and Bender, Michael A. and Demaine, Erik and Leiserson, Charles and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {1862-4405},
URL = {urn:nbn:de:0030-drops-1576},
PUBLISHER = {Schloss Dagstuhl},
YEAR = {2004},
DATE = {2005},
SERIES = {Dagstuhl Seminar Proceedings},
VOLUME = {04301},
ADDRESS = {Wadern, Germany},
}

Endnote

%0 Conference Proceedings
%E Lars, Arge
%E Bender, Michael A.
%E Demaine, Erik
%E Leiserson, Charles
%E Mehlhorn, Kurt
%+ External Organizations
External Organizations
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Cache-Oblivious and Cache-Aware Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0027-D634-3
%U urn:nbn:de:0030-drops-1576
%I Schloss Dagstuhl
%D 2005
%B Cache-Oblivious and Cache-Aware Algorithms (Dagstuhl Seminar 04301)
%Z date of event: 2004-07-18 - 2004-07-23
%D 2004
%C Wadern, Germany
%S Dagstuhl Seminar Proceedings
%V 04301
%@ false
%U http://drops.dagstuhl.de/opus/volltexte/2005/157/http://drops.dagstuhl.de/doku/urheberrecht1.html

[198]

K. Mehlhorn and D. Michail, “Network Problems with Non-Polynomial Weights And Applications.” 2005.

Export

BibTeX

@misc{MehlhornNetwork2005,
TITLE = {Network Problems with Non-Polynomial Weights And Applications},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios},
YEAR = {2005},
}

Endnote

%0 Report
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Network Problems with Non-Polynomial Weights And Applications :
%U http://hdl.handle.net/11858/00-001M-0000-002B-4DD1-6
%D 2005

[199]

K. Mehlhorn and D. Michail, “Implementing Minimum Cycle Basis Algorithms,” in Experimental and Efficient Algorithms, 4th InternationalWorkshop, WEA 2005, 2005.

Abstract

In this paper we consider the problem of computing a minimum cycle basis of an
undirected graph $G = (V,E)$ with $n$ vertices and $m$ edges. We describe an
efficient implementation of an $O(m^3 + mn^2\log n)$ algorithm presented
in~\cite{PINA95}. For sparse graphs this is the currently best known algorithm.
This algorithm's running time can be partitioned into two parts
with time $O(m^3)$ and $O( m^2n + mn^2 \log n)$ respectively.
Our experimental findings imply that the true bottleneck of a
sophisticated implementation is the $O( m^2 n + mn^2 \log n)$ part. A
straightforward implementation would require $\Omega(nm)$ shortest path
computations, thus we develop several heuristics in order to get a practical
algorithm. Our experiments show that in random graphs our techniques result in
a significant speedup.
Based on our experimental observations, we combine the two fundamentally
different approaches to compute a minimum cycle basis used
in~\cite{PINA95,KMMP04} and~\cite{HOR87,MATR02}, to obtain a new hybrid
algorithm with running time
$O( m^2 n^2 )$. The hybrid algorithm is very efficient in practice for random
dense unweighted graphs.
Finally, we compare these two algorithms with a number of previous
implementations for finding a minimum cycle basis in an undirected graph.

Export

BibTeX

@inproceedings{MM05,
TITLE = {Implementing Minimum Cycle Basis Algorithms},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios},
EDITOR = {Nikoletseas, Sotiris},
LANGUAGE = {eng},
ISBN = {3-540-25920-1},
LOCALID = {Local-ID: C1256428004B93B8-AC9540F47424F880C1256FD400450006-MM05},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
ABSTRACT = {In this paper we consider the problem of computing a minimum cycle basis of an undirected graph $G = (V,E)$ with $n$ vertices and $m$ edges. We describe an efficient implementation of an $O(m^3 + mn^2\log n)$ algorithm presented in~\cite{PINA95}. For sparse graphs this is the currently best known algorithm. This algorithm's running time can be partitioned into two parts with time $O(m^3)$ and $O( m^2n + mn^2 \log n)$ respectively. Our experimental findings imply that the true bottleneck of a sophisticated implementation is the $O( m^2 n + mn^2 \log n)$ part. A straightforward implementation would require $\Omega(nm)$ shortest path computations, thus we develop several heuristics in order to get a practical algorithm. Our experiments show that in random graphs our techniques result in a significant speedup. Based on our experimental observations, we combine the two fundamentally different approaches to compute a minimum cycle basis used in~\cite{PINA95,KMMP04} and~\cite{HOR87,MATR02}, to obtain a new hybrid algorithm with running time $O( m^2 n^2 )$. The hybrid algorithm is very efficient in practice for random dense unweighted graphs. Finally, we compare these two algorithms with a number of previous implementations for finding a minimum cycle basis in an undirected graph.},
BOOKTITLE = {Experimental and Efficient Algorithms, 4th InternationalWorkshop, WEA 2005},
PAGES = {32--43},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3503},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%E Nikoletseas, Sotiris
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Implementing Minimum Cycle Basis Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-26BF-0
%F EDOC: 279141
%F OTHER: Local-ID: C1256428004B93B8-AC9540F47424F880C1256FD400450006-MM05
%D 2005
%B Untitled Event
%Z date of event: 2005-05-10 -
%C Santorini, Greece
%X In this paper we consider the problem of computing a minimum cycle basis of an
undirected graph $G = (V,E)$ with $n$ vertices and $m$ edges. We describe an
efficient implementation of an $O(m^3 + mn^2\log n)$ algorithm presented
in~\cite{PINA95}. For sparse graphs this is the currently best known algorithm.
This algorithm's running time can be partitioned into two parts
with time $O(m^3)$ and $O( m^2n + mn^2 \log n)$ respectively.
Our experimental findings imply that the true bottleneck of a
sophisticated implementation is the $O( m^2 n + mn^2 \log n)$ part. A
straightforward implementation would require $\Omega(nm)$ shortest path
computations, thus we develop several heuristics in order to get a practical
algorithm. Our experiments show that in random graphs our techniques result in
a significant speedup.
Based on our experimental observations, we combine the two fundamentally
different approaches to compute a minimum cycle basis used
in~\cite{PINA95,KMMP04} and~\cite{HOR87,MATR02}, to obtain a new hybrid
algorithm with running time
$O( m^2 n^2 )$. The hybrid algorithm is very efficient in practice for random
dense unweighted graphs.
Finally, we compare these two algorithms with a number of previous
implementations for finding a minimum cycle basis in an undirected graph.
%B Experimental and Efficient Algorithms, 4th InternationalWorkshop, WEA 2005
%P 32 - 43
%I Springer
%@ 3-540-25920-1
%B Lecture Notes in Computer Science
%N 3503

[200]

K. Mehlhorn, “Minimum Cycle Bases and Surface Reconstruction,” in Graph Drawing (GD 2005), Limerick, Ireland, 2005.

Export

BibTeX

@inproceedings{mehlhorn05,
TITLE = {Minimum Cycle Bases and Surface Reconstruction},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-31425-3},
DOI = {10.1007/11618058_55},
PUBLISHER = {Springer},
YEAR = {2005},
DATE = {2005},
BOOKTITLE = {Graph Drawing (GD 2005)},
EDITOR = {Healy, Patrick and Nikolo, Nikola S.},
PAGES = {532--532},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3843},
ADDRESS = {Limerick, Ireland},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Minimum Cycle Bases and Surface Reconstruction :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-E9EE-8
%R 10.1007/11618058_55
%D 2005
%B GD 2005
%Z date of event: -
%C Limerick, Ireland
%B Graph Drawing
%E Healy, Patrick; Nikolo, Nikola S.
%P 532 - 532
%I Springer
%@ 3-540-31425-3
%B Lecture Notes in Computer Science
%N 3843

[201]

K. Mehlhorn, U. Waldmann, and R. Wilhelm, “Harald Ganzinger : 31.10.1950 - 3.6.2004,” Jahrbuch der Max-Planck-Gesellschaft, 2005.

Export

BibTeX

@article{mehlhorn05a,
TITLE = {{Harald Ganzinger : 31.10.1950 -- 3.6.2004}},
AUTHOR = {Mehlhorn, Kurt and Waldmann, Uwe and Wilhelm, Reinhard},
LANGUAGE = {deu},
PUBLISHER = {MPG},
ADDRESS = {M{\"u}nchen},
YEAR = {2005},
DATE = {2005},
JOURNAL = {Jahrbuch der Max-Planck-Gesellschaft},
PAGES = {107--108},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Waldmann, Uwe
%A Wilhelm, Reinhard
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Automation of Logic, MPI for Informatics, Max Planck Society
External Organizations
%T Harald Ganzinger : 31.10.1950 - 3.6.2004 :
%G deu
%U http://hdl.handle.net/11858/00-001M-0000-0029-2A45-F
%D 2005
%J Jahrbuch der Max-Planck-Gesellschaft
%O MAX-PLANCK-GES JAHRB
%& 107
%P 107 - 108
%I MPG
%C München

2004

[202]

E. Althaus, F. Eisenbrand, S. Funke, and K. Mehlhorn, “Point Containment in the Integer Hull of a Polyhedron,” in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04), New Orleans, USA, 2004.

Abstract

We show that the point containment problem in the integer hull of a
polyhedron, which is defined by $m$ inequalities, with
coefficients of at most $\varphi$ bits can be solved in
time $O(m+\varphi)$ in the two-dimensional case and in expected time
$O(m+\varphi^2 \log m)$ in any fixed dimension. This improves on the
algorithm which is based on the equivalence of separation and
optimization in the general case and on a direct algorithm (SODA 97)
for the two-dimensional case.

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BibTeX

@inproceedings{AEFM2004-NWG,
TITLE = {Point Containment in the Integer Hull of a Polyhedron},
AUTHOR = {Althaus, Ernst and Eisenbrand, Friedrich and Funke, Stefan and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {0-89871-558-X},
LOCALID = {Local-ID: C1256BDD00205AD6-5A66A234AFD82E2DC1256E0C0040AD33-AEFM2004-NWG},
PUBLISHER = {ACM},
YEAR = {2004},
DATE = {2004},
ABSTRACT = {We show that the point containment problem in the integer hull of a polyhedron, which is defined by $m$ inequalities, with coefficients of at most $\varphi$ bits can be solved in time $O(m+\varphi)$ in the two-dimensional case and in expected time $O(m+\varphi^2 \log m)$ in any fixed dimension. This improves on the algorithm which is based on the equivalence of separation and optimization in the general case and on a direct algorithm (SODA 97) for the two-dimensional case.},
BOOKTITLE = {Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04)},
PAGES = {929--933},
ADDRESS = {New Orleans, USA},
}

Endnote

%0 Conference Proceedings
%A Althaus, Ernst
%A Eisenbrand, Friedrich
%A Funke, Stefan
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Discrete Optimization, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Point Containment in the Integer Hull of a Polyhedron :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2BA9-D
%F EDOC: 241594
%F OTHER: Local-ID: C1256BDD00205AD6-5A66A234AFD82E2DC1256E0C0040AD33-AEFM2004-NWG
%D 2004
%B Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms
%Z date of event: 2004-01-11 -
%C New Orleans, USA
%X We show that the point containment problem in the integer hull of a
polyhedron, which is defined by $m$ inequalities, with
coefficients of at most $\varphi$ bits can be solved in
time $O(m+\varphi)$ in the two-dimensional case and in expected time
$O(m+\varphi^2 \log m)$ in any fixed dimension. This improves on the
algorithm which is based on the equivalence of separation and
optimization in the general case and on a direct algorithm (SODA 97)
for the two-dimensional case.
%B Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04)
%P 929 - 933
%I ACM
%@ 0-89871-558-X

[203]

B. Aranov, T. Asano, N. Katoh, K. Mehlhorn, and T. Tokuyama, “Polyline Fitting of Planar Points Under Min-sum Criteria,” in Algorithms and Computation: 15th International Symposium, ISAAC 2004, 2004.

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BibTeX

@inproceedings{Mehlhorn2004PolylineApprox,
TITLE = {Polyline Fitting of Planar Points Under Min-sum Criteria},
AUTHOR = {Aranov, Boris and Asano, Tetsuo and Katoh, Naoki and Mehlhorn, Kurt and Tokuyama, Takeshi},
EDITOR = {Fleischer, Rudolf and Trippen, Gerhard},
LANGUAGE = {eng},
ISBN = {3-540-24131-0},
LOCALID = {Local-ID: C1256428004B93B8-3575485A1DE95D4CC1256FC500831646-Mehlhorn2004PolylineApprox},
PUBLISHER = {Springer},
YEAR = {2004},
DATE = {2004},
BOOKTITLE = {Algorithms and Computation: 15th International Symposium, ISAAC 2004},
PAGES = {77--88},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3341},
}

Endnote

%0 Conference Proceedings
%A Aranov, Boris
%A Asano, Tetsuo
%A Katoh, Naoki
%A Mehlhorn, Kurt
%A Tokuyama, Takeshi
%E Fleischer, Rudolf
%E Trippen, Gerhard
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Polyline Fitting of Planar Points Under Min-sum Criteria :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2AFE-8
%F EDOC: 232077
%F OTHER: Local-ID: C1256428004B93B8-3575485A1DE95D4CC1256FC500831646-Mehlhorn2004PolylineApprox
%D 2004
%B Untitled Event
%Z date of event: 2004-12-20 -
%C HongKong, China
%B Algorithms and Computation: 15th International Symposium, ISAAC 2004
%P 77 - 88
%I Springer
%@ 3-540-24131-0
%B Lecture Notes in Computer Science
%N 3341

[204]

H. Bast, K. Mehlhorn, G. Schäfer, and H. Tamaki, “Matching Algorithms Are Fast in Sparse Random Graphs,” in 21st Annual Symposium on Theoretical Aspects of Computer Science (STACS-04), 2004.

Abstract

We present an improved average case analysis of the maximum
cardinality matching problem. We show that in a bipartite or
general random graph on n vertices, with high probability every nonmaximum
matching has an augmenting path of length O(log n). This implies that
augmenting path algorithms like the Hopcroft Karp algorithm for bipartite
graphs and the Micali Vazirani algorithm for general graphs, which have a worst
case running time of O(mpn), run in time O(mlog n) with high probability, where
m is the number of edges in the graph. Motwani proved these results for random
graphs when the average degree is at least ln(n) [Average Case Analysis of
Algorithms for Matchings and Related Problems, Journal of the ACM, 41(6),
1994]. Our
results hold, if only the average degree is a large enough constant. At the
same time we simplify the analysis of Motwani.

Export

BibTeX

@inproceedings{bast04stacs,
TITLE = {Matching Algorithms Are Fast in Sparse Random Graphs},
AUTHOR = {Bast, Holger and Mehlhorn, Kurt and Sch{\"a}fer, Guido and Tamaki, Hisao},
EDITOR = {Diekert, Volker and Habib, Michel},
LANGUAGE = {eng},
ISBN = {3-540-21236-1},
LOCALID = {Local-ID: C1256428004B93B8-1F79D167AE1C3869C1256F9500480213-bast04stacs},
PUBLISHER = {Springer},
YEAR = {2004},
DATE = {2004},
ABSTRACT = {We present an improved average case analysis of the maximum cardinality matching problem. We show that in a bipartite or general random graph on n vertices, with high probability every nonmaximum matching has an augmenting path of length O(log n). This implies that augmenting path algorithms like the Hopcroft Karp algorithm for bipartite graphs and the Micali Vazirani algorithm for general graphs, which have a worst case running time of O(mpn), run in time O(mlog n) with high probability, where m is the number of edges in the graph. Motwani proved these results for random graphs when the average degree is at least ln(n) [Average Case Analysis of Algorithms for Matchings and Related Problems, Journal of the ACM, 41(6), 1994]. Our results hold, if only the average degree is a large enough constant. At the same time we simplify the analysis of Motwani.},
BOOKTITLE = {21st Annual Symposium on Theoretical Aspects of Computer Science (STACS-04)},
PAGES = {81--92},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2996},
}

Endnote

%0 Conference Proceedings
%A Bast, Holger
%A Mehlhorn, Kurt
%A Schäfer, Guido
%A Tamaki, Hisao
%E Diekert, Volker
%E Habib, Michel
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Matching Algorithms Are Fast in Sparse Random Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-290E-8
%F EDOC: 231169
%F OTHER: Local-ID: C1256428004B93B8-1F79D167AE1C3869C1256F9500480213-bast04stacs
%D 2004
%B Untitled Event
%Z date of event: 2004-03-25 -
%C Montpellier, France
%X We present an improved average case analysis of the maximum
cardinality matching problem. We show that in a bipartite or
general random graph on n vertices, with high probability every nonmaximum
matching has an augmenting path of length O(log n). This implies that
augmenting path algorithms like the Hopcroft Karp algorithm for bipartite
graphs and the Micali Vazirani algorithm for general graphs, which have a worst
case running time of O(mpn), run in time O(mlog n) with high probability, where
m is the number of edges in the graph. Motwani proved these results for random
graphs when the average degree is at least ln(n) [Average Case Analysis of
Algorithms for Matchings and Related Problems, Journal of the ACM, 41(6),
1994]. Our
results hold, if only the average degree is a large enough constant. At the
same time we simplify the analysis of Motwani.
%B 21st Annual Symposium on Theoretical Aspects of Computer Science (STACS-04)
%P 81 - 92
%I Springer
%@ 3-540-21236-1
%B Lecture Notes in Computer Science
%N 2996

[205]

E. Berberich, A. Eigenwillig, M. Hemmer, S. Hert, L. Kettner, K. Mehlhorn, J. Reichel, S. Schmitt, E. Schömer, D. Weber, and N. Wolpert, “EXACUS : Efficient and Exact Algorithms for Curves and Surfaces,” INRIA, Sophia Antipolis, ECG-TR-361200-02, 2004.

Export

BibTeX

@techreport{Berberich_ECG-TR-361200-02,
TITLE = {{EXACUS} : Efficient and Exact Algorithms for Curves and Surfaces},
AUTHOR = {Berberich, Eric and Eigenwillig, Arno and Hemmer, Michael and Hert, Susan and Kettner, Lutz and Mehlhorn, Kurt and Reichel, Joachim and Schmitt, Susanne and Sch{\"o}mer, Elmar and Weber, Dennis and Wolpert, Nicola},
LANGUAGE = {eng},
NUMBER = {ECG-TR-361200-02},
INSTITUTION = {INRIA},
ADDRESS = {Sophia Antipolis},
YEAR = {2004},
DATE = {2004},
TYPE = {ECG Technical Report},
EDITOR = {{Effective Computational Geometry for Curves and Surfaces}},
}

Endnote

%0 Report
%A Berberich, Eric
%A Eigenwillig, Arno
%A Hemmer, Michael
%A Hert, Susan
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Reichel, Joachim
%A Schmitt, Susanne
%A Schömer, Elmar
%A Weber, Dennis
%A Wolpert, Nicola
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T EXACUS : Efficient and Exact Algorithms for Curves and Surfaces :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2B89-6
%F EDOC: 237751
%Y INRIA
%C Sophia Antipolis
%D 2004
%Z name of event: Untitled Event
%Z date of event: -
%Z place of event:
%P 8 p.
%B ECG Technical Report

[206]

E. Berberich, A. Eigenwillig, I. Emiris, E. Fogel, M. Hemmer, D. Halperin, A. Kakargias, L. Kettner, K. Mehlhorn, S. Pion, E. Schömer, M. Teillaud, R. Wein, and N. Wolpert, “An empirical comparison of software for constructing arrangements of curved arcs,” INRIA, Sophia Antipolis, ECG-TR-361200-01, 2004.

Export

BibTeX

@techreport{Berberich_ECG-TR-361200-01,
TITLE = {An empirical comparison of software for constructing arrangements of curved arcs},
AUTHOR = {Berberich, Eric and Eigenwillig, Arno and Emiris, Ioannis and Fogel, Efraim and Hemmer, Michael and Halperin, Dan and Kakargias, Athanasios and Kettner, Lutz and Mehlhorn, Kurt and Pion, Sylvain and Sch{\"o}mer, Elmar and Teillaud, Monique and Wein, Ron and Wolpert, Nicola},
LANGUAGE = {eng},
NUMBER = {ECG-TR-361200-01},
INSTITUTION = {INRIA},
ADDRESS = {Sophia Antipolis},
YEAR = {2004},
DATE = {2004},
TYPE = {ECG Technical Report},
EDITOR = {{Effective Computational Geometry for Curves and Surfaces}},
}

Endnote

%0 Report
%A Berberich, Eric
%A Eigenwillig, Arno
%A Emiris, Ioannis
%A Fogel, Efraim
%A Hemmer, Michael
%A Halperin, Dan
%A Kakargias, Athanasios
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Pion, Sylvain
%A Schömer, Elmar
%A Teillaud, Monique
%A Wein, Ron
%A Wolpert, Nicola
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T An empirical comparison of software for constructing arrangements of curved arcs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2B87-A
%F EDOC: 237743
%Y INRIA
%C Sophia Antipolis
%D 2004
%Z name of event: Untitled Event
%Z date of event: -
%Z place of event:
%P 11 p.
%B ECG Technical Report

[207]

S. Funke, K. Mehlhorn, S. Schmitt, C. Burnikel, R. Fleischer, and S. Schirra, “The LEDA class real number - extended version,” INRIA, Sophia Antipolis, ECG-TR-363110-01, 2004.

Export

BibTeX

@techreport{Funke_ECG-TR-363110-01,
TITLE = {The {LEDA} class real number -- extended version},
AUTHOR = {Funke, Stefan and Mehlhorn, Kurt and Schmitt, Susanne and Burnikel, Christoph and Fleischer, Rudolf and Schirra, Stefan},
LANGUAGE = {eng},
NUMBER = {ECG-TR-363110-01},
INSTITUTION = {INRIA},
ADDRESS = {Sophia Antipolis},
YEAR = {2004},
DATE = {2004},
TYPE = {ECG Technical Report},
EDITOR = {{Effective Computational Geometry for Curves and Surfaces}},
}

Endnote

%0 Report
%A Funke, Stefan
%A Mehlhorn, Kurt
%A Schmitt, Susanne
%A Burnikel, Christoph
%A Fleischer, Rudolf
%A Schirra, Stefan
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The LEDA class real number - extended version :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2B8C-F
%F EDOC: 237780
%Y INRIA
%C Sophia Antipolis
%D 2004
%Z name of event: Untitled Event
%Z date of event: -
%Z place of event:
%P 2 p.
%B ECG Technical Report

[208]

T. Kavitha, K. Mehlhorn, D. Michail, and K. Paluch, “Strongly Stable Matchings in Time O(nm) and Extension to the Hospitals-Residents Problem,” in STACS 2004, 21st Annual Symposium on Theoretical Aspects of Computer Science, Montpellier, France, 2004.

Export

BibTeX

@inproceedings{Michail2004b,
TITLE = {Strongly Stable Matchings in Time O(nm) and Extension to the Hospitals-Residents Problem},
AUTHOR = {Kavitha, Telikepalli and Mehlhorn, Kurt and Michail, Dimitrios and Paluch, Katarzyna},
LANGUAGE = {eng},
ISBN = {3-540-21236-1},
DOI = {10.1007/978-3-540-24749-4_20},
PUBLISHER = {Springer},
YEAR = {2004},
DATE = {2004},
BOOKTITLE = {STACS 2004, 21st Annual Symposium on Theoretical Aspects of Computer Science},
EDITOR = {Diekert, Volker and Habib, Michel},
PAGES = {222--233},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2996},
ADDRESS = {Montpellier, France},
}

Endnote

%0 Conference Proceedings
%A Kavitha, Telikepalli
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Paluch, Katarzyna
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
%T Strongly Stable Matchings in Time O(nm) and Extension to the Hospitals-Residents Problem :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2952-A
%F EDOC: 231218
%R 10.1007/978-3-540-24749-4_20
%D 2004
%B 21st Annual Symposium on Theoretical Aspects of Computer Science
%Z date of event: 2004-03-25 -
%C Montpellier, France
%B STACS 2004
%E Diekert, Volker; Habib, Michel
%P 222 - 233
%I Springer
%@ 3-540-21236-1
%B Lecture Notes in Computer Science
%N 2996

[209]

L. Kettner, K. Mehlhorn, S. Pion, S. Schirra, and C. Yap, “Classroom Examples of Robustness Problems in Geometric Computations,” in Algorithms – ESA 2004, Bergen, Norway, 2004.

Abstract

The algorithms of computational geometry are designed for a<br>machine model with exact real arithmetic. Substituting floating point<br>arithmetic for the assumed real arithmetic may cause implementations to<br>fail. Although this is well known, there is no comprehensive documentation of<br>what can go wrong and why. <br>In this extended abstract, we study a simple<br>incremental algorithm for planar convex hulls and give examples which make<br>the algorithm fail in all possible ways.<br>We also show how to construct failure-examples<br>semi-systematically and discuss the geometry of the floating point<br>implementation of the orientation predicate. We hope that our work will be<br>useful for teaching computational geometry. The full<br>paper is available<br>at~\url{www.mpi-sb.mpg.de/~mehlhorn/ftp/ClassRoomExamples.ps}. It contains<br>further examples, more theory, and color pictures. We strongly recommend to read<br> the<br>full paper instead of this extended abstract.

Export

BibTeX

@inproceedings{Kettner_ESA2004,
TITLE = {Classroom Examples of Robustness Problems in Geometric Computations},
AUTHOR = {Kettner, Lutz and Mehlhorn, Kurt and Pion, Sylvain and Schirra, Stefan and Yap, Chee},
EDITOR = {Albers, Susanne and Radzik, Tomasz},
LANGUAGE = {eng},
ISBN = {3-540-23025-4},
LOCALID = {Local-ID: C1256428004B93B8-433D199DFE8DDF4DC1256F170032471A-Kettner2004Classroom},
PUBLISHER = {Springer},
YEAR = {2004},
DATE = {2004},
ABSTRACT = {The algorithms of computational geometry are designed for a<br>machine model with exact real arithmetic. Substituting floating point<br>arithmetic for the assumed real arithmetic may cause implementations to<br>fail. Although this is well known, there is no comprehensive documentation of<br>what can go wrong and why. <br>In this extended abstract, we study a simple<br>incremental algorithm for planar convex hulls and give examples which make<br>the algorithm fail in all possible ways.<br>We also show how to construct failure-examples<br>semi-systematically and discuss the geometry of the floating point<br>implementation of the orientation predicate. We hope that our work will be<br>useful for teaching computational geometry. The full<br>paper is available<br>at~\url{www.mpi-sb.mpg.de/~mehlhorn/ftp/ClassRoomExamples.ps}. It contains<br>further examples, more theory, and color pictures. We strongly recommend to read<br> the<br>full paper instead of this extended abstract.},
BOOKTITLE = {Algorithms -- ESA 2004},
DEBUG = {editor: Albers, Susanne; editor: Radzik, Thomasz},
PAGES = {702--713},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3221},
ADDRESS = {Bergen, Norway},
}

Endnote

%0 Conference Proceedings
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Pion, Sylvain
%A Schirra, Stefan
%A Yap, Chee
%E Albers, Susanne
%E Radzik, Tomasz
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Classroom Examples of Robustness Problems in Geometric Computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2A4C-5
%F EDOC: 231814
%F OTHER: Local-ID: C1256428004B93B8-433D199DFE8DDF4DC1256F170032471A-Kettner2004Classroom
%D 2004
%B 12th Annual European Symposium on Algorithms
%Z date of event: 2004-09-14 - 2004-09-17
%C Bergen, Norway
%X The algorithms of computational geometry are designed for a<br>machine model with exact real arithmetic. Substituting floating point<br>arithmetic for the assumed real arithmetic may cause implementations to<br>fail. Although this is well known, there is no comprehensive documentation of<br>what can go wrong and why. <br>In this extended abstract, we study a simple<br>incremental algorithm for planar convex hulls and give examples which make<br>the algorithm fail in all possible ways.<br>We also show how to construct failure-examples<br>semi-systematically and discuss the geometry of the floating point<br>implementation of the orientation predicate. We hope that our work will be<br>useful for teaching computational geometry. The full<br>paper is available<br>at~\url{www.mpi-sb.mpg.de/~mehlhorn/ftp/ClassRoomExamples.ps}. It contains<br>further examples, more theory, and color pictures. We strongly recommend to read<br> the<br>full paper instead of this extended abstract.
%B Algorithms – ESA 2004
%E Albers, Susanne; Radzik, Thomasz
%P 702 - 713
%I Springer
%@ 3-540-23025-4
%B Lecture Notes in Computer Science
%N 3221

[210]

L. Kettner, K. Mehlhorn, S. Pion, S. Schirra, and C. Yap, “Classroom examples of robustness problems in geometric computations,” INRIA, Sophia Antipolis, ECG-TR-363100-01, 2004.

Export

BibTeX

@techreport{Kettner_ECG-TR-363100-01,
TITLE = {Classroom examples of robustness problems in geometric computations},
AUTHOR = {Kettner, Lutz and Mehlhorn, Kurt and Pion, Sylvain and Schirra, Stefan and Yap, Chee},
LANGUAGE = {eng},
NUMBER = {ECG-TR-363100-01},
INSTITUTION = {INRIA},
ADDRESS = {Sophia Antipolis},
YEAR = {2004},
DATE = {2004},
TYPE = {ECG Technical Report},
EDITOR = {{Effective Computational Geometry for Curves and Surfaces}},
VOLUME = {3221},
}

Endnote

%0 Report
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Pion, Sylvain
%A Schirra, Stefan
%A Yap, Chee
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Classroom examples of robustness problems in geometric computations :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2B92-0
%F EDOC: 237797
%Y INRIA
%C Sophia Antipolis
%D 2004
%Z name of event: Untitled Event
%Z date of event: -
%Z place of event:
%P 12 p.
%B ECG Technical Report
%N 3221

[211]

W. Krandick and K. Mehlhorn, “New bounds for the Descartes method,” Drexel University, Philadelphia, Pa., DU-CS-04-04, 2004.

Export

BibTeX

@techreport{Krandick_DU-CS-04-04,
TITLE = {New bounds for the Descartes method},
AUTHOR = {Krandick, Werner and Mehlhorn, Kurt},
LANGUAGE = {eng},
NUMBER = {DU-CS-04-04},
INSTITUTION = {Drexel University},
ADDRESS = {Philadelphia, Pa.},
YEAR = {2004},
DATE = {2004},
TYPE = {Drexel University / Department of Computer Science:Technical Report},
EDITOR = {{Drexel University {\textless}Philadelphia, Pa.{\textgreater} / Department of Computer Science}},
}

Endnote

%0 Report
%A Krandick, Werner
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T New bounds for the Descartes method :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2B99-2
%F EDOC: 237829
%Y Drexel University
%C Philadelphia, Pa.
%D 2004
%P 18 p.
%B Drexel University / Department of Computer Science:Technical Report

[212]

K. Mehlhorn, D. Michail, K. Telikepalli, and K. Paluch, “A Faster Algorithm for Minimum Cycle Basis of Graphs,” in Automata, languages and programming : 31st International Colloquium, ICALP 2004, 2004.

Abstract

In this paper we consider the problem of computing a minimum cycle basis in a
graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative
weights on them. The previous best result for this problem was an
$O(m^{\omega}n)$ algorithm, where $\omega$ is the best exponent of matrix
multiplication. It is presently known that $\omega < 2.376$.
We obtain an $O(m^2n + mn^2\log n)$ algorithm for this problem. Our algorithm
also uses fast matrix multiplication.
When the edge weights are integers, we have an $O(m^2n)$ algorithm.
For unweighted graphs which are reasonably dense, our
algorithm runs in $O(m^{\omega})$ time. For any $\epsilon > 0$,
we also design a $1+\epsilon$ approximation algorithm to compute a cycle basis
which is at most $1+\epsilon$ times the weight of a minimum cycle basis. The
running time of this algorithm is
$O(\frac{m^{\omega}}{\epsilon}\log(W/{\epsilon}))$ for
reasonably dense graphs, where $W$ is the largest edge weight.

Export

BibTeX

@inproceedings{KMMP2004c,
TITLE = {A Faster Algorithm for Minimum Cycle Basis of Graphs},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios and Telikepalli, Kavitha and Paluch, Katarzyna},
EDITOR = {D{\'i}az, Josep and Karhum{\"a}ki, Juhani and Lepist{\"o}, Arto and Sannella, Donald},
LANGUAGE = {eng},
ISSN = {0302-9743},
LOCALID = {Local-ID: C1256428004B93B8-158CD04BC22EDE8AC1256F4F00523BF7-KMMP2004c},
PUBLISHER = {Springer},
YEAR = {2004},
DATE = {2004},
ABSTRACT = {In this paper we consider the problem of computing a minimum cycle basis in a graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative weights on them. The previous best result for this problem was an $O(m^{\omega}n)$ algorithm, where $\omega$ is the best exponent of matrix multiplication. It is presently known that $\omega < 2.376$. We obtain an $O(m^2n + mn^2\log n)$ algorithm for this problem. Our algorithm also uses fast matrix multiplication. When the edge weights are integers, we have an $O(m^2n)$ algorithm. For unweighted graphs which are reasonably dense, our algorithm runs in $O(m^{\omega})$ time. For any $\epsilon > 0$, we also design a $1+\epsilon$ approximation algorithm to compute a cycle basis which is at most $1+\epsilon$ times the weight of a minimum cycle basis. The running time of this algorithm is $O(\frac{m^{\omega}}{\epsilon}\log(W/{\epsilon}))$ for reasonably dense graphs, where $W$ is the largest edge weight.},
BOOKTITLE = {Automata, languages and programming : 31st International Colloquium, ICALP 2004},
PAGES = {846--857},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {3142},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Telikepalli, Kavitha
%A Paluch, Katarzyna
%E Díaz, Josep
%E Karhumäki, Juhani
%E Lepistö, Arto
%E Sannella, Donald
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Max Planck Society
%T A Faster Algorithm for Minimum Cycle Basis of Graphs :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2A07-0
%F EDOC: 231968
%F OTHER: Local-ID: C1256428004B93B8-158CD04BC22EDE8AC1256F4F00523BF7-KMMP2004c
%D 2004
%B Untitled Event
%Z date of event: 2004-07-12 -
%C Turku, Finland
%X In this paper we consider the problem of computing a minimum cycle basis in a
graph $G$ with $m$ edges and $n$ vertices. The edges of $G$ have non-negative
weights on them. The previous best result for this problem was an
$O(m^{\omega}n)$ algorithm, where $\omega$ is the best exponent of matrix
multiplication. It is presently known that $\omega < 2.376$.
We obtain an $O(m^2n + mn^2\log n)$ algorithm for this problem. Our algorithm
also uses fast matrix multiplication.
When the edge weights are integers, we have an $O(m^2n)$ algorithm.
For unweighted graphs which are reasonably dense, our
algorithm runs in $O(m^{\omega})$ time. For any $\epsilon > 0$,
we also design a $1+\epsilon$ approximation algorithm to compute a cycle basis
which is at most $1+\epsilon$ times the weight of a minimum cycle basis. The
running time of this algorithm is
$O(\frac{m^{\omega}}{\epsilon}\log(W/{\epsilon}))$ for
reasonably dense graphs, where $W$ is the largest edge weight.
%B Automata, languages and programming : 31st International Colloquium, ICALP 2004
%P 846 - 857
%I Springer
%B Lecture Notes in Computer Science
%N 3142
%@ false

[213]

K. Mehlhorn, D. Michail, K. Telikepalli, R. Irving, and K. Paluch, “Rank-Maximal Matchings,” in Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04), 2004.

Export

BibTeX

@inproceedings{Michail2004a,
TITLE = {Rank-Maximal Matchings},
AUTHOR = {Mehlhorn, Kurt and Michail, Dimitrios and Telikepalli, Kavitha and Irving, Robert and Paluch, Katarzyna},
LANGUAGE = {eng},
ISBN = {0-89871-558-X},
LOCALID = {Local-ID: C1256428004B93B8-9704AA318902D853C1256EA90050697A-Michail2004a},
PUBLISHER = {ACM},
YEAR = {2004},
DATE = {2004},
BOOKTITLE = {Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04)},
PAGES = {68--75},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%A Michail, Dimitrios
%A Telikepalli, Kavitha
%A Irving, Robert
%A Paluch, Katarzyna
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Rank-Maximal Matchings :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2B10-1
%F EDOC: 231957
%F OTHER: Local-ID: C1256428004B93B8-9704AA318902D853C1256EA90050697A-Michail2004a
%I ACM
%D 2004
%B Untitled Event
%Z date of event: 2004-01-11 -
%C New Orleans, USA
%B Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-04)
%P 68 - 75
%I ACM
%@ 0-89871-558-X

2003

[214]

E. Althaus, D. Duchier, A. Koller, K. Mehlhorn, J. Niehren, and S. Thiel, “An Efficient Graph Algorithm for Dominance Constraints,” Journal of Algorithms, vol. 48, no. 1, 2003.

Export

BibTeX

@article{ADKMNT03:dominance,
TITLE = {An Efficient Graph Algorithm for Dominance Constraints},
AUTHOR = {Althaus, Ernst and Duchier, Denys and Koller, Alexander and Mehlhorn, Kurt and Niehren, Joachim and Thiel, Sven},
LANGUAGE = {eng},
ISSN = {0196-6774},
DOI = {10.1016/S0196-6774(03)00050-6},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2003},
DATE = {2003},
JOURNAL = {Journal of Algorithms},
VOLUME = {48},
NUMBER = {1},
PAGES = {194--219},
}

Endnote

%0 Journal Article
%A Althaus, Ernst
%A Duchier, Denys
%A Koller, Alexander
%A Mehlhorn, Kurt
%A Niehren, Joachim
%A Thiel, Sven
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T An Efficient Graph Algorithm for Dominance Constraints :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2C1E-E
%F EDOC: 201974
%R 10.1016/S0196-6774(03)00050-6
%7 2003
%D 2003
%* Review method: peer-reviewed
%J Journal of Algorithms
%V 48
%N 1
%& 194
%P 194 - 219
%I Elsevier
%C Amsterdam
%@ false

[215]

C. Banderier, R. Beier, and K. Mehlhorn, “Smoothed Analysis of Three Combinatorial Problems,” in Mathematical foundations of computer science 2003 : 28th International Symposium, MFCS 2003, Bratislava, Slovak Republic, 2003.

Abstract

Smoothed analysis combines elements over worst-case and
average case analysis. For an instance $x$, the smoothed complexity is the
average complexity of an instance obtained from $x$ by a perturbation. The
smoothed complexity of a problem is the worst smoothed complexity of any
instance. Spielman and Teng introduced this notion for
continuous problems. We apply the concept to combinatorial problems and study
the smoothed complexity of three classical discrete problems: quicksort,
left-to-right maxima counting, and shortest paths.

Export

BibTeX

@inproceedings{Beier2003a,
TITLE = {Smoothed Analysis of Three Combinatorial Problems},
AUTHOR = {Banderier, Cyril and Beier, Rene and Mehlhorn, Kurt},
EDITOR = {Rovan, Branislav and Vojt{\'a}{\v s}, Peter},
LANGUAGE = {eng},
ISBN = {3-540-40671-9},
LOCALID = {Local-ID: C1256428004B93B8-09CF39E77E5072D5C1256E140059E6C7-Beier2003a},
PUBLISHER = {Springer},
YEAR = {2003},
DATE = {2003},
ABSTRACT = {Smoothed analysis combines elements over worst-case and average case analysis. For an instance $x$, the smoothed complexity is the average complexity of an instance obtained from $x$ by a perturbation. The smoothed complexity of a problem is the worst smoothed complexity of any instance. Spielman and Teng introduced this notion for continuous problems. We apply the concept to combinatorial problems and study the smoothed complexity of three classical discrete problems: quicksort, left-to-right maxima counting, and shortest paths.},
BOOKTITLE = {Mathematical foundations of computer science 2003 : 28th International Symposium, MFCS 2003},
PAGES = {198--207},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2747},
ADDRESS = {Bratislava, Slovak Republic},
}

Endnote

%0 Conference Proceedings
%A Banderier, Cyril
%A Beier, Rene
%A Mehlhorn, Kurt
%E Rovan, Branislav
%E Vojtáš, Peter
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Smoothed Analysis of Three Combinatorial Problems :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2E18-C
%F EDOC: 202044
%F OTHER: Local-ID: C1256428004B93B8-09CF39E77E5072D5C1256E140059E6C7-Beier2003a
%D 2003
%B MFCS 2003
%Z date of event: 2003-08-25 - 2003-08-29
%C Bratislava, Slovak Republic
%X Smoothed analysis combines elements over worst-case and
average case analysis. For an instance $x$, the smoothed complexity is the
average complexity of an instance obtained from $x$ by a perturbation. The
smoothed complexity of a problem is the worst smoothed complexity of any
instance. Spielman and Teng introduced this notion for
continuous problems. We apply the concept to combinatorial problems and study
the smoothed complexity of three classical discrete problems: quicksort,
left-to-right maxima counting, and shortest paths.
%B Mathematical foundations of computer science 2003 : 28th International Symposium, MFCS 2003
%P 198 - 207
%I Springer
%@ 3-540-40671-9
%B Lecture Notes in Computer Science
%N 2747

[216]

H. Bast, K. Mehlhorn, G. Schäfer, and H. Tamaki, “A Heuristic for Dijkstra’s Algorithm With Many Targets and its Use in Weighted Matching Algorithms,” Algorithmica, vol. 36, 2003.

Abstract

We consider the single-source many-targets shortest-path (SSMTSP) problem in
directed graphs with non-negative
edge weights. A source node $s$ and a target set $T$ is specified and the goal
is to compute a shortest path from $s$ to a node in $T$.
Our interest in the shortest path problem with many targets stems from its use
in weighted bipartite matching algorithms. A weighted bipartite matching in a
graph with $n$ nodes on each side reduces to $n$ SSMTSP problems, where the
number
of targets varies between $n$ and $1$.
The SSMTSP problem can be solved by Dijkstra's algorithm. We describe a
heuristic
that leads to a significant improvement in running time for the weighted
matching
problem; in our experiments a speed-up by up to a factor of 12 was achieved.
We also present a partial analysis that gives some theoretical support for our
experimental findings.

Export

BibTeX

@article{BMST03,
TITLE = {A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms},
AUTHOR = {Bast, Holger and Mehlhorn, Kurt and Sch{\"a}fer, Guido and Tamaki, Hisao},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-6EE356D1B824CE83C1256D03005D49A1-BMST03},
YEAR = {2003},
DATE = {2003},
ABSTRACT = {We consider the single-source many-targets shortest-path (SSMTSP) problem in directed graphs with non-negative edge weights. A source node $s$ and a target set $T$ is specified and the goal is to compute a shortest path from $s$ to a node in $T$. Our interest in the shortest path problem with many targets stems from its use in weighted bipartite matching algorithms. A weighted bipartite matching in a graph with $n$ nodes on each side reduces to $n$ SSMTSP problems, where the number of targets varies between $n$ and $1$. The SSMTSP problem can be solved by Dijkstra's algorithm. We describe a heuristic that leads to a significant improvement in running time for the weighted matching problem; in our experiments a speed-up by up to a factor of 12 was achieved. We also present a partial analysis that gives some theoretical support for our experimental findings.},
JOURNAL = {Algorithmica},
VOLUME = {36},
PAGES = {75--88},
}

Endnote

%0 Journal Article
%A Bast, Holger
%A Mehlhorn, Kurt
%A Schäfer, Guido
%A Tamaki, Hisao
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T A Heuristic for Dijkstra's Algorithm With Many Targets and its Use in Weighted Matching Algorithms :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2C0B-7
%F EDOC: 201912
%F OTHER: Local-ID: C1256428004B93B8-6EE356D1B824CE83C1256D03005D49A1-BMST03
%D 2003
%* Review method: peer-reviewed
%X We consider the single-source many-targets shortest-path (SSMTSP) problem in
directed graphs with non-negative
edge weights. A source node $s$ and a target set $T$ is specified and the goal
is to compute a shortest path from $s$ to a node in $T$.
Our interest in the shortest path problem with many targets stems from its use
in weighted bipartite matching algorithms. A weighted bipartite matching in a
graph with $n$ nodes on each side reduces to $n$ SSMTSP problems, where the
number
of targets varies between $n$ and $1$.
The SSMTSP problem can be solved by Dijkstra's algorithm. We describe a
heuristic
that leads to a significant improvement in running time for the weighted
matching
problem; in our experiments a speed-up by up to a factor of 12 was achieved.
We also present a partial analysis that gives some theoretical support for our
experimental findings.
%J Algorithmica
%V 36
%& 75
%P 75 - 88

[217]

M. Dhiflaoui, S. Funke, C. Kwappik, K. Mehlhorn, M. Seel, E. Schömer, R. Schulte, and D. Weber, “Certifying and Repairing Solutions to Large LPs - How Good are LP-Solvers?,” in Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-03), Baltimore, USA, 2003.

Export

BibTeX

@inproceedings{dfkmsssw2003,
TITLE = {Certifying and Repairing Solutions to Large {LP}s -- How Good are {LP}-Solvers?},
AUTHOR = {Dhiflaoui, Marcel and Funke, Stefan and Kwappik, Carsten and Mehlhorn, Kurt and Seel, Michael and Sch{\"o}mer, Elmar and Schulte, Ralph and Weber, Dennis},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-F01D6B673BC1A37AC1256CC200533255-dfkmsssw2003},
PUBLISHER = {ACM},
YEAR = {2003},
DATE = {2003},
BOOKTITLE = {Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-03)},
PAGES = {255--256},
ADDRESS = {Baltimore, USA},
}

Endnote

%0 Conference Proceedings
%A Dhiflaoui, Marcel
%A Funke, Stefan
%A Kwappik, Carsten
%A Mehlhorn, Kurt
%A Seel, Michael
%A Schömer, Elmar
%A Schulte, Ralph
%A Weber, Dennis
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying and Repairing Solutions to Large LPs - How Good are LP-Solvers? :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2C74-C
%F EDOC: 201850
%F OTHER: Local-ID: C1256428004B93B8-F01D6B673BC1A37AC1256CC200533255-dfkmsssw2003
%D 2003
%B SODA 2003
%Z date of event: 2003-01-12 - 2003-01-14
%C Baltimore, USA
%B Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-03)
%P 255 - 256
%I ACM

[218]

M. Granados, P. Hachenberger, S. Hert, L. Kettner, K. Mehlhorn, and M. Seel, “Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation,” in Algorithms - ESA 2003: 11th Annual European Symposium, Budapest, Hungary, 2003.

Abstract

We describe a data structure for three-dimensional Nef complexes, algorithms
for boolean operations on them, and our implementation of data structure and
algorithms. Nef polyhedra were introduced by W. Nef in his seminal 1978 book on
polyhedra. They are the closure of half-spaces under boolean operations and can
represent non-manifold situations, open and closed boundaries, and mixed
dimensional complexes. Our focus lies on the generality of the data structure,
the completeness of the algorithms, and the exactness and efficiency of the
implementation. In particular, all degeneracies are handled.

Export

BibTeX

@inproceedings{ghhkms-bo3ds-03,
TITLE = {Boolean Operations on {3D} Selective Nef Complexes: Data Structure, Algorithms, and Implementation},
AUTHOR = {Granados, Miguel and Hachenberger, Peter and Hert, Susan and Kettner, Lutz and Mehlhorn, Kurt and Seel, Michael},
EDITOR = {Di Battista, Giuseppe and Zwick, Uri},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-D0F786CC6723EB72C1256E2F0050063D-ghhkms-bo3ds-03},
PUBLISHER = {Springer},
YEAR = {2003},
DATE = {2003},
ABSTRACT = {We describe a data structure for three-dimensional Nef complexes, algorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were introduced by W. Nef in his seminal 1978 book on polyhedra. They are the closure of half-spaces under boolean operations and can represent non-manifold situations, open and closed boundaries, and mixed dimensional complexes. Our focus lies on the generality of the data structure, the completeness of the algorithms, and the exactness and efficiency of the implementation. In particular, all degeneracies are handled.},
BOOKTITLE = {Algorithms -- ESA 2003: 11th Annual European Symposium},
PAGES = {654--666},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2832},
ADDRESS = {Budapest, Hungary},
}

Endnote

%0 Conference Proceedings
%A Granados, Miguel
%A Hachenberger, Peter
%A Hert, Susan
%A Kettner, Lutz
%A Mehlhorn, Kurt
%A Seel, Michael
%E Di Battista, Giuseppe
%E Zwick, Uri
%+ Computer Graphics, MPI for Informatics, Max Planck Society
International Max Planck Research School, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2C67-A
%F EDOC: 201891
%F OTHER: Local-ID: C1256428004B93B8-D0F786CC6723EB72C1256E2F0050063D-ghhkms-bo3ds-03
%D 2003
%B ESA 2003
%Z date of event: 2003-09-16 - 2003-09-19
%C Budapest, Hungary
%X We describe a data structure for three-dimensional Nef complexes, algorithms
for boolean operations on them, and our implementation of data structure and
algorithms. Nef polyhedra were introduced by W. Nef in his seminal 1978 book on
polyhedra. They are the closure of half-spaces under boolean operations and can
represent non-manifold situations, open and closed boundaries, and mixed
dimensional complexes. Our focus lies on the generality of the data structure,
the completeness of the algorithms, and the exactness and efficiency of the
implementation. In particular, all degeneracies are handled.
%B Algorithms - ESA 2003: 11th Annual European Symposium
%P 654 - 666
%I Springer
%B Lecture Notes in Computer Science
%N 2832

[219]

D. Kratsch, R. McConnell, K. Mehlhorn, and J. Spinrad, “Certifying algorithms for recognizing interval graphs and permutation graph,” in Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-03), Baltimore, 2003.

Export

BibTeX

@inproceedings{Kratsch-et-al:interval,
TITLE = {Certifying algorithms for recognizing interval graphs and permutation graph},
AUTHOR = {Kratsch, Dieter and McConnell, R. and Mehlhorn, Kurt and Spinrad, J.},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-90DAACD3D4A0C6A8C1256E20004505E1-xxxx},
PUBLISHER = {ACM},
YEAR = {2004},
DATE = {2003},
BOOKTITLE = {Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-03)},
PAGES = {158--167},
ADDRESS = {Baltimore},
}

Endnote

%0 Conference Proceedings
%A Kratsch, Dieter
%A McConnell, R.
%A Mehlhorn, Kurt
%A Spinrad, J.
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Certifying algorithms for recognizing interval graphs and permutation graph :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2C71-1
%F EDOC: 201954
%F OTHER: Local-ID: C1256428004B93B8-90DAACD3D4A0C6A8C1256E20004505E1-xxxx
%D 2003
%B SODA 2003
%Z date of event: 2004-01-12 - 2004-01-14
%C Baltimore
%B Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA-03)
%P 158 - 167
%I ACM

[220]

S. Kwek and K. Mehlhorn, “Optimal Search for Rationals,” Information Processing Letters, vol. 86, no. 1, 2003.

Export

BibTeX

@article{KwekMehlhorn2003,
TITLE = {Optimal Search for Rationals},
AUTHOR = {Kwek, St. and Mehlhorn, Kurt},
LANGUAGE = {eng},
ISSN = {0020-0190},
DOI = {10.1016/S0020-0190(02)00455-6},
LOCALID = {Local-ID: C1256428004B93B8-7BB72399D6E566FBC1256E2000449EF3-xxxx},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
YEAR = {2003},
DATE = {2003},
JOURNAL = {Information Processing Letters},
VOLUME = {86},
NUMBER = {1},
PAGES = {23--26},
}

Endnote

%0 Journal Article
%A Kwek, St.
%A Mehlhorn, Kurt
%+ External Organizations
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Optimal Search for Rationals :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2DAA-A
%F EDOC: 201934
%F OTHER: Local-ID: C1256428004B93B8-7BB72399D6E566FBC1256E2000449EF3-xxxx
%R 10.1016/S0020-0190(02)00455-6
%D 2003
%* Review method: peer-reviewed
%J Information Processing Letters
%V 86
%N 1
%& 23
%P 23 - 26
%I Elsevier
%C Amsterdam
%@ false

[221]

K. Mehlhorn, “The Reliable Algorithmic Software Challenge RASC,” in Experimental and efficient algorithms (WEA 2003), Ascona, Switzerland, 2003.

Abstract

Algorithms are the heart of computer science. They make systems work. The
theory of algorithms, i.e., their design and their analysis, is a highly
developed part of theoretical computer science [7].

Export

BibTeX

@inproceedings{mehlhorn03,
TITLE = {The Reliable Algorithmic Software Challenge {RASC}},
AUTHOR = {Mehlhorn, Kurt},
LANGUAGE = {eng},
ISBN = {3-540-40205-5},
DOI = {10.1007/3-540-36477-3_19},
PUBLISHER = {Springer},
YEAR = {2003},
DATE = {2003},
ABSTRACT = {Algorithms are the heart of computer science. They make systems work. The theory of algorithms, i.e., their design and their analysis, is a highly developed part of theoretical computer science [7].},
BOOKTITLE = {Experimental and efficient algorithms (WEA 2003)},
EDITOR = {Jansen, Klaus and Margraf, Marian and Mastrolli, Monaldo and Rolim, Jos{\'e} D. P.},
PAGES = {222--222},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2647},
ADDRESS = {Ascona, Switzerland},
}

Endnote

%0 Conference Proceedings
%A Mehlhorn, Kurt
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T The Reliable Algorithmic Software Challenge RASC :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-0019-EE28-B
%R 10.1007/3-540-36477-3_19
%D 2003
%B WEA 2003
%Z date of event: 2003-05-26 - 2003-05-28
%C Ascona, Switzerland
%X Algorithms are the heart of computer science. They make systems work. The
theory of algorithms, i.e., their design and their analysis, is a highly
developed part of theoretical computer science [7].
%B Experimental and efficient algorithms
%E Jansen, Klaus; Margraf, Marian; Mastrolli, Monaldo; Rolim, José D. P.
%P 222 - 222
%I Springer
%@ 3-540-40205-5
%B Lecture Notes in Computer Science
%N 2647

[222]

K. Mehlhorn, “The Reliable Algorithmic Software Challenge RASC Dedicated to Thomas Ottmann on the Occasion of His 60th Birthday,” in Computer Science in Perspective, R. Klein, H.-W. Six, and L. Wegner, Eds. Berlin, Germany: Springer, 2003.

Export

BibTeX

@incollection{KM03b,
TITLE = {The Reliable Algorithmic Software Challenge {RASC} Dedicated to {Thomas Ottmann} on the Occasion of His 60th Birthday},
AUTHOR = {Mehlhorn, Kurt},
EDITOR = {Klein, Rolf and Six, Hans-Werner and Wegner, Lutz},
LANGUAGE = {eng},
ISBN = {3-540-00579-X},
DOI = {10.1007/3-540-36477-3_19},
LOCALID = {Local-ID: A185BAA82C068ABBC1256E1D0048A367-KM03b},
PUBLISHER = {Springer},
ADDRESS = {Berlin, Germany},
YEAR = {2003},
DATE = {2003},
BOOKTITLE = {Computer Science in Perspective},
DEBUG = {editor: Klein, Rolf; editor: Six, Hans-Werner; editor: Wegner, Lutz},
PAGES = {255--263},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2598},
}

Endnote

%0 Book Section
%A Mehlhorn, Kurt
%E Klein, Rolf
%E Six, Hans-Werner
%E Wegner, Lutz
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
External Organizations
External Organizations
External Organizations
%T The Reliable Algorithmic Software Challenge RASC Dedicated to Thomas Ottmann on the Occasion of His 60th Birthday :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2E5E-0
%F EDOC: 201874
%F OTHER: Local-ID: A185BAA82C068ABBC1256E1D0048A367-KM03b
%R 10.1007/3-540-36477-3_19
%D 2003
%B Computer Science in Perspective
%E Klein, Rolf; Six, Hans-Werner; Wegner, Lutz
%P 255 - 263
%I Springer
%C Berlin, Germany
%@ 3-540-00579-X
%S Lecture Notes in Computer Science
%N 2598

[223]

K. Mehlhorn and M. Seel, “Infimaximal frames: A technique for making lines look like segments,” International Journal of Computational Geometry & Applications, vol. 13, 2003.

Export

BibTeX

@article{Mehlhorn157,
TITLE = {Infimaximal frames: A technique for making lines look like segments},
AUTHOR = {Mehlhorn, Kurt and Seel, Michael},
LANGUAGE = {eng},
LOCALID = {Local-ID: C1256428004B93B8-A569041E8BA55F92C1256E2000412135-Mehlhorn157},
YEAR = {2003},
DATE = {2003},
JOURNAL = {International Journal of Computational Geometry \& Applications},
VOLUME = {13},
PAGES = {241--255},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Seel, Michael
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Infimaximal frames: A technique for making lines look like segments :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2D40-7
%F EDOC: 201910
%F OTHER: Local-ID: C1256428004B93B8-A569041E8BA55F92C1256E2000412135-Mehlhorn157
%D 2003
%* Review method: peer-reviewed
%J International Journal of Computational Geometry & Applications
%V 13
%& 241
%P 241 - 255

[224]

K. Mehlhorn and P. Sanders, “Scanning Multiple Sequences via Cache Memory,” Algorithmica, vol. 35, no. 1, 2003.

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BibTeX

@article{Mehlhorn-Schirra_Algorithmica2003,
TITLE = {Scanning Multiple Sequences via Cache Memory},
AUTHOR = {Mehlhorn, Kurt and Sanders, Peter},
LANGUAGE = {eng},
ISSN = {0178-4617},
DOI = {10.1007/s00453-002-0993-2},
LOCALID = {Local-ID: C1256428004B93B8-E0E179EACB48E199C1256E1D00390DB7-MehSan03},
PUBLISHER = {Springer-Verlag},
ADDRESS = {New York, NY},
YEAR = {2003},
DATE = {2003},
JOURNAL = {Algorithmica},
VOLUME = {35},
NUMBER = {1},
PAGES = {75--93},
}

Endnote

%0 Journal Article
%A Mehlhorn, Kurt
%A Sanders, Peter
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T Scanning Multiple Sequences via Cache Memory :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-2DFE-E
%F EDOC: 201936
%F OTHER: Local-ID: C1256428004B93B8-E0E179EACB48E199C1256E1D00390DB7-MehSan03
%R 10.1007/s00453-002-0993-2
%D 2003
%* Review method: peer-reviewed
%J Algorithmica
%V 35
%N 1
%& 75
%P 75 - 93
%I Springer-Verlag
%C New York, NY
%@ false
%U https://rdcu.be/dwDg1

2002

[225]

E. Althaus, A. Bockmayr, M. Elf, T. Kasper, M. Jünger, and K. Mehlhorn, “SCIL - Symbolic Constraints in Integer Linear Programming.,” in Algorithms - ESA 2002 : 10th Annual European Symposium, Rom, Italy, 2002.

Abstract

We describe a new software system SCIL that introduces symbolic constraints
into branch-and-cut-and-price algorithms for integer linear programs. Symbolic
constraints are known from constraint programming and contribute significantly
to the expressive power, ease of use, and efficiency of constraint programming
systems.

Export

BibTeX

@inproceedings{Althaus2002,
TITLE = {{SCIL} -- Symbolic Constraints in Integer Linear Programming.},
AUTHOR = {Althaus, Ernst and Bockmayr, Alexander and Elf, Matthias and Kasper, Thomas and J{\"u}nger, Michael and Mehlhorn, Kurt},
EDITOR = {M{\"o}hring, Rolf and Raman, Rajeev},
LANGUAGE = {eng},
ISBN = {3-540-44180-8},
LOCALID = {Local-ID: C1256428004B93B8-5EA058E323C086ACC1256C9300519510-Althaus2002},
PUBLISHER = {Springer},
YEAR = {2002},
DATE = {2002},
ABSTRACT = {We describe a new software system SCIL that introduces symbolic constraints into branch-and-cut-and-price algorithms for integer linear programs. Symbolic constraints are known from constraint programming and contribute significantly to the expressive power, ease of use, and efficiency of constraint programming systems.},
BOOKTITLE = {Algorithms -- ESA 2002 : 10th Annual European Symposium},
PAGES = {75--87},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {2461},
ADDRESS = {Rom, Italy},
}

Endnote

%0 Conference Proceedings
%A Althaus, Ernst
%A Bockmayr, Alexander
%A Elf, Matthias
%A Kasper, Thomas
%A Jünger, Michael
%A Mehlhorn, Kurt
%E Möhring, Rolf
%E Raman, Rajeev
%+ Algorithms and Complexity, MPI for Informatics, Max Planck Society
Programming Logics, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Programming Logics, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
Algorithms and Complexity, MPI for Informatics, Max Planck Society
%T SCIL - Symbolic Constraints in Integer Linear Programming. :
%G eng
%U http://hdl.handle.net/11858/00-001M-0000-000F-3067-E
%F EDOC: 202066
%F OTHER: Local-ID: C1256428004B93B8-5EA058E323C086ACC1256C9300519510-Althaus2002
%D 2002
%B ESA 2002
%Z date of event: 2002-09-17 - 2002-09-21
%C Rom, Italy
%X We describe a new software system SCIL that introduces symbolic constraints
into branch-and-cut-and-price algorithms for integer linear programs. Symbolic
constraints are known from constraint programming and contribute significantly
to the expressive power, ease of use, and efficiency of constraint programming
systems.
%B Algorithms - ESA 2002 : 10th Annual European Symposium
%P 75 - 87
%I Springer
%@ 3-540-44180-8
%B Lecture Notes in Computer Science
%N 2461

[226]

E. Berberich, A. Eigenwillig, M. Hemmer, S. Hert, K. Mehlhorn, and E. Schömer, “A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons,” in Algorithms - ESA 2002 : 10th Annual European Symposium, Rome, Italy, 2002.