Publications

%0 Conference Proceedings %A Arunachalam, Srinivasan %A Chakraborty, Sourav %A Koucký, Michal %A Saurabh, Nitin %A de Wolf, Ronald %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Improved Bounds on Fourier Entropy and Min-entropy : %G eng %U http://hdl.handle.net/21.11116/0000-0006-97AB-F %R 10.4230/LIPIcs.STACS.2020.45 %U urn:nbn:de:0030-drops-119062 %D 2020 %B 37th International Symposium on Theoretical Aspects of Computer Science %Z date of event: 2020-03-10 - 2020-03-13 %C Montpellier, France %B 37th International Symposium on Theoretical Aspects of Computer Science %E Paul, Christophe; Bläser, Markus %P 1 - 19 %Z sequence number: 45 %I Schloss Dagstuhl %@ 978-3-95977-140-5 %B Leibniz International Proceedings in Informatics %N 154 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/11906/

%0 Conference Proceedings %A Becker, Ruben %A Emek, Yuval %A Lenzen, Christoph %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Low Diameter Graph Decompositions by Approximate Distance Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-A7A7-2 %R 10.4230/LIPIcs.ITCS.2020.50 %U urn:nbn:de:0030-drops-117355 %D 2020 %B 11th Innovations in Theoretical Computer Science Conference %Z date of event: 2020-01-12 - 2020-01-14 %C Seattle, WA, USA %B 11th Innovations in Theoretical Computer Science Conference %E Vidick, Thomas %Z sequence number: 50 %I Schloss Dagstuhl %@ 978-3-95977-134-4 %B Leibniz International Proceedings in Informatics %N 151 %@ false %U https://drops.dagstuhl.de/opus/volltexte/2020/11735/https://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Journal Article %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-Containing Sorting via Parallel Prefix Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-9E7F-C %R 10.1109/TC.2019.2939818 %7 2020 %D 2020 %J IEEE Transactions on Computers %V 69 %N 2 %& 198 %P 198 - 211 %I IEEE %C Piscataway, NJ %@ false

%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

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

%0 Journal Article %A Jain, Pallavi %A Kanesh, Lawqueen %A Misra, Pranabendu %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Conflict Free Version of Covering Problems on Graphs: Classical and Parameterized : %G eng %U http://hdl.handle.net/21.11116/0000-0006-90BA-5 %R 10.1007/s00224-019-09964-6 %7 2020 %D 2020 %J Theory of Computing Systems %I Springer %C New York, NY %@ false

%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

%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon : %G eng %U http://hdl.handle.net/21.11116/0000-0006-8E04-6 %R 10.1007/s00454-019-00063-4 %7 2019 %D 2020 %J Discrete & Computational Geometry %V 63 %N 2 %& 418 %P 418 - 454 %I Springer %@ false

%0 Journal Article %A Oulasvirta, Antti %A Dayama, Niraj Ramesh %A Shiripour, Morteza %A John, Maximilian %A Karrenbauer, Andreas %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Combinatorial Optimization of Graphical User Interface Designs : %G eng %U http://hdl.handle.net/21.11116/0000-0006-99BA-C %R 10.1109/JPROC.2020.2969687 %7 2020 %D 2020 %J Proceedings of the IEEE %O Proc. IEEE %V 108 %N 3 %& 434 %P 434 - 464 %I IEEE %C New York, N.Y. %@ false

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

%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

%0 Conference Proceedings %A Roth, Marc %A Wellnitz, Philip %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting and Finding Homomorphisms is Universal for Parameterized Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0005-8665-2 %R 10.1137/1.9781611975994.133 %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 2161 - 2180 %I SIAM %@ 978-1-61197-599-4

%0 Conference Proceedings %A Saurabh, Saket %A Souza, Uéverton dos Santos %A Tale, Prafullkumar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Parameterized Complexity of Grid Contraction : %G eng %U http://hdl.handle.net/21.11116/0000-0006-8BA6-2 %R 10.4230/LIPIcs.SWAT.2020.34 %U urn:nbn:de:0030-drops-122810 %D 2020 %B 17th Scandinavian Symposiumand Workshops on Algorithm Theory %Z date of event: 2020-06-22 - 2020-06-24 %C órshavn, Faroe Islands %B 17th Scandinavian Symposium and Workshops on Algorithm Theory %E Albers, Susanne %Z sequence number: 34 %I Schloss Dagstuhl %@ 978-3-95977-150-4 %B Leibniz International Proceedings in Informatics %N 162 %U https://drops.dagstuhl.de/opus/volltexte/2020/12281/

%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T SETH-Based Lower Bounds for Subset Sum and Bicriteria Path : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E12-8 %R 10.1137/1.9781611975482.3 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 41 - 57 %I SIAM %@ 978-1-61197-548-2

%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 library of correct and efficient data structures, graph algorithms and geometric algorithms. We report on the use of formal program verification to achieve an even higher level of trustworthiness. Specifically, we report on an ongoing and largely finished verification of the blossom-shrinking algorithm for maximum cardinality matching. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Logic in Computer Science, cs.LO,Computer Science, Software Engineering, cs.SE

%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

%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

%0 Journal Article %A Ahn, Hee-Kap %A Oh, E. %A Schlipf, Lena %A Stehn, Fabian %A Strash, Darren %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T On Romeo and Juliet Problems: Minimizing Distance-to-Sight : %G eng %U http://hdl.handle.net/21.11116/0000-0004-E582-6 %R 10.1016/j.comgeo.2019.07.003 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 84 %& 12 %P 12 - 21 %I Elsevier %C Amsterdam %@ false

%0 Journal Article %A Ahn, Hee-Kap %A Ahn, Taehoon %A Bae, Sang Won %A Choi, Jongmin %A Kim, Mincheol %A Oh, Eunjin %A Shin, Chan-Su %A Yoon, Sang Duk %+ External Organizations External Organizations External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Minimum-width Annulus with Outliers: Circular, Square, and Rectangular Cases : %G eng %U http://hdl.handle.net/21.11116/0000-0003-4FD4-6 %R 10.1016/j.ipl.2019.01.004 %7 2019 %D 2019 %J Information Processing Letters %V 145 %& 16 %P 16 - 23 %I Elsevier %C Amsterdam %@ false

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

%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

%0 Journal Article %A Amiri, Saeed Akhoondian %A Kreutzer, Stephan %A Marx, Dániel %A Rabinovich, Roman %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Routing with Congestion in Acyclic Digraphs : %G eng %U http://hdl.handle.net/21.11116/0000-0004-B836-0 %R 10.1016/j.ipl.2019.105836 %7 2019 %D 2019 %J Information Processing Letters %V 151 %Z sequence number: 105836 %I Elsevier %@ false

%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Dudycz, Szymon %A Parham, Mahmoud %A Schmid, Stefan %A Wiederrecht, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T On Polynomial-Time Congestion-Free Software-Defined Network Updates : %G eng %U http://hdl.handle.net/21.11116/0000-0004-B83C-A %R 10.23919/IFIPNetworking.2019.8816833 %D 2019 %B IFIP Networking Conference %Z date of event: 2019-05-20 - 2019-05-22 %C Warsaw, Poland %B IFIP Networking Conference %I IEEE

%0 Journal Article %A Amiri, Saeed Akhoondian %A Schmid, Stefan %A Siebertz, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Distributed Dominating Set Approximations beyond Planar Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0004-8335-C %R 10.1145/3326170 %7 2019 %D 2019 %J ACM Transactions on Algorithms %V 15 %N 3 %Z sequence number: 39 %I ACM %C New York, NY %@ false

%0 Journal Article %A Antoniadis, Antonios %A Huang, Chien-Chung %A Ott, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Fully Polynomial-Time Approximation Scheme for Speed Scaling with Sleep State : %G eng %U http://hdl.handle.net/21.11116/0000-0004-AAC7-C %R 10.1007/s00453-019-00596-3 %7 2019 %D 2019 %J Algorithmica %V 81 %N 9 %& 3725 %P 3725 - 3745 %I Springer %C New York, NY %@ false

%0 Journal Article %A Antoniadis, Antonios %A Barcelo, Neal %A Nugent, Michael %A Pruhs, Kirk %A Scquizzato, Michele %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations %T A o(n)-Competitive Deterministic Algorithm for Online Matching on a Line : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7DA-B %R 10.1007/s00453-019-00565-w %7 2019 %D 2019 %J Algorithmica %V 81 %N 7 %& 2917 %P 2917 - 2933 %I Springer %C New York, NY %@ false

%0 Conference Proceedings %A Antoniadis, Antonios %A Fleszar, Krzysztof %A Hoeksma, Ruben %A Schewior, Kevin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A PTAS for Euclidean TSP with Hyperplane Neighborhoods : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F3A-B %R 10.1137/1.9781611975482.67 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 1089 - 1105 %I SIAM %@ 978-1-61197-548-2

%0 Journal Article %A Ballard, Grey %A Ikenmeyer, Christian %A Landsberg, J. M. %A Ryder, Nick %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AB17-4 %R 10.1016/j.jpaa.2018.10.014 %7 2018 %D 2019 %J Journal of Pure and Applied Algebra %O J. Pure Appl. Algebra %V 223 %N 8 %& 3205 %P 3205 - 3224 %I North-Holland %C Amsterdam %@ false

%0 Conference Proceedings %A Balliu, Alkida %A Hirvonen, Juho %A Lenzen, Christoph %A Olivetti, Dennis %A Suomela, Jukka %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Locality of Not-so-Weak Coloring : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1BF2-C %R 10.1007/978-3-030-24922-9_3 %D 2019 %B 26th International Colloquium on Structural Information and Communication Complexity %Z date of event: 2019-07-01 - 2019-07-04 %C L’Aquila, Italy %B Structural Information and Communication Complexity %E Censor-Hillel, Keren; Flammini, Michele %P 37 - 51 %I Springer %@ 978-3-030-24921-2 978-3-030-24922-9 %B Lecture Notes in Computer Science %N 11639

%0 Report %A Balliu, Alkida %A Hirvonen, Juho %A Lenzen, Christoph %A Olivetti, Dennis %A Suomela, Jukka %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Locality of Not-So-Weak Coloring : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B39F-0 %U http://arxiv.org/abs/1904.05627 %D 2019 %X Many graph problems are locally checkable: a solution is globally feasible if it looks valid in all constant-radius neighborhoods. This idea is formalized in the concept of locally checkable labelings (LCLs), introduced by Naor and Stockmeyer (1995). Recently, Chang et al. (2016) showed that in bounded-degree graphs, every LCL problem belongs to one of the following classes: - "Easy": solvable in $O(\log^* n)$ rounds with both deterministic and randomized distributed algorithms. - "Hard": requires at least $\Omega(\log n)$ rounds with deterministic and $\Omega(\log \log n)$ rounds with randomized distributed algorithms. Hence for any parameterized LCL problem, when we move from local problems towards global problems, there is some point at which complexity suddenly jumps from easy to hard. For example, for vertex coloring in $d$-regular graphs it is now known that this jump is at precisely $d$ colors: coloring with $d+1$ colors is easy, while coloring with $d$ colors is hard. However, it is currently poorly understood where this jump takes place when one looks at defective colorings. To study this question, we define $k$-partial $c$-coloring as follows: nodes are labeled with numbers between $1$ and $c$, and every node is incident to at least $k$ properly colored edges. It is known that $1$-partial $2$-coloring (a.k.a. weak $2$-coloring) is easy for any $d \ge 1$. As our main result, we show that $k$-partial $2$-coloring becomes hard as soon as $k \ge 2$, no matter how large a $d$ we have. We also show that this is fundamentally different from $k$-partial $3$-coloring: no matter which $k \ge 3$ we choose, the problem is always hard for $d = k$ but it becomes easy when $d \gg k$. The same was known previously for partial $c$-coloring with $c \ge 4$, but the case of $c < 4$ was open. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Computational Complexity, cs.CC

%0 Conference Proceedings %A Ban, Frank %A Bhattiprolu, Vijay %A Bringmann, Karl %A Kolev, Pavel %A Lee, Euiwoong %A Woodruff, David %+ 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 %T A PTAS for l_p-Low Rank Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E0E-E %R 10.1137/1.9781611975482.47 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 747 - 766 %I SIAM %@ 978-1-61197-548-2

%0 Journal Article %A Becchetti, Luca %A Clementi, Andrea %A Natale, Emanuele %A Pasquale, Francesco %A Posta, Gustavo %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Self-Stabilizing Repeated Balls-into-Bins : %G eng %U http://hdl.handle.net/21.11116/0000-0002-F6C1-E %R 10.1007/s00446-017-0320-4 %7 2017 %D 2019 %J Distributed Computing %V 32 %N 1 %& 59 %P 59 - 68 %I Springer International %C Berlin %@ false

%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 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 %J Theoretical Computer Science %V 773 %& 79 %P 79 - 106 %I Elsevier %C Amsterdam %@ false

%0 Report %A Becker, Ruben %A Emek, Yuval %A Lenzen, Christoph %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Low Diameter Graph Decompositions by Approximate Distance Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1C65-B %U http://arxiv.org/abs/1909.09002 %D 2019 %X In many models for large-scale computation, decomposition of the problem is key to efficient algorithms. For distance-related graph problems, it is often crucial that such a decomposition results in clusters of small diameter, while the probability that an edge is cut by the decomposition scales linearly with the length of the edge. There is a large body of literature on low diameter graph decomposition with small edge cutting probabilities, with all existing techniques heavily building on single source shortest paths (SSSP) computations. Unfortunately, in many theoretical models for large-scale computations, the SSSP task constitutes a complexity bottleneck. Therefore, it is desirable to replace exact SSSP computations with approximate ones. However this imposes a fundamental challenge since the existing constructions of such decompositions inherently rely on the subtractive form of the triangle inequality. The current paper overcomes this obstacle by developing a technique termed blurry ball growing. By combining this technique with a clever algorithmic idea of Miller et al. (SPAA 13), we obtain a construction of low diameter decompositions with small edge cutting probabilities which replaces exact SSSP computations by (a small number of) approximate ones. The utility of our approach is showcased by deriving efficient algorithms that work in the Congest, PRAM, and semi-streaming models of computation. As an application, we obtain metric tree embedding algorithms in the vein of Bartal (FOCS 96) whose computational complexities in these models are optimal up to polylogarithmic factors. Our embeddings have the additional useful property that the tree can be mapped back to the original graph such that each edge is "used" only O(log n) times, which is of interest for capacitated problems and simulating Congest algorithms on the tree into which the graph is embedded. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Conference Proceedings %A Becker, Ruben %A Emek, Yuval %A Ghaffari, Mohsen %A Lenzen, C. %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Distributed Algorithms for Low Stretch Spanning Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1C52-0 %R 10.4230/LIPIcs.DISC.2019.4 %U urn:nbn:de:0030-drops-113116 %D 2019 %B 33rd International Symposiumon Distributed Computing %Z date of event: 2019-10-14 - 2019-10-18 %C Budapest, Hungary %B 33rd International Symposiumon Distributed Computing %E Suomela, Jukka %P 1 - 14 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-126-9 %B Leibniz International Proceedings in Informatics %N 146 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/11311http://drops.dagstuhl.de/doku/urheberrecht1.html

%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

%0 Journal Article %A Beyersdorff, Olaf %A Chew, Leroy %A Sreenivasaiah, Karteek %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Game Characterisation of Tree-like Q-Resolution Size : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5F80-F %R 10.1016/j.jcss.2016.11.011 %7 2017 %D 2019 %J Journal of Computer and System Sciences %V 104 %& 82 %P 82 - 101 %I Elsevier %C Amsterdam %@ false

%0 Conference Proceedings %A Bhargava, Vishwas %A Bl&#228;ser, Markus %A Jindal, Gorav %A Pandey, Anurag %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Deterministic PTAS for the Algebraic Rank of Bounded Degree Polynomials : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ABAD-B %R 10.1137/1.9781611975482.41 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 647 - 661 %I SIAM %@ 978-1-61197-548-2

%0 Report %A Bl&#228;ser, Markus %A Ikenmeyer, Christian %A Lysikov, Vladimir %A Pandey, Anurag %A Schreyer, Frank-Olaf %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Variety Membership Testing, Algebraic Natural Proofs, and Geometric Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1D77-6 %U http://arxiv.org/abs/1911.02534 %D 2019 %X We study the variety membership testing problem in the case when the variety is given as an orbit closure and the ambient space is the set of all 3-tensors. The first variety that we consider is the slice rank variety, which consists of all 3-tensors of slice rank at most $r$. We show that the membership testing problem for the slice rank variety is $\NP$-hard. While the slice rank variety is a union of orbit closures, we define another variety, the minrank variety, expressible as a single orbit closure. Our next result is the $\NP$-hardness of membership testing in the minrank variety, hence we establish the $\NP$-hardness of the orbit closure containment problem for 3-tensors. Algebraic natural proofs were recently introduced by Forbes, Shpilka and Volk and independently by Grochow, Kumar, Saks and Saraf. Bl\"aser et al. gave a version of an algebraic natural proof barrier for the matrix completion problem which relies on $\coNP \subseteq \exists \BPP$. It implied that constructing equations for the corresponding variety should be hard. We generalize their approach to work with any family of varieties for which the membership problem is $\NP$-hard and for which we can efficiently generate a dense subset. Therefore, a similar barrier holds for the slice rank and the minrank varieties, too. This allows us to set up the slice rank and the minrank varieties as a test-bed for geometric complexity theory (GCT). We determine the stabilizers of the tensors that generate the orbit closures of the two varieties and prove that these tensors are almost characterized by their symmetries. We prove several nontrivial equations for both the varieties using different GCT methods. Many equations also work in the regime where membership testing in the slice rank or minrank varieties is $\NP$-hard. We view this as a promising sign that the GCT approach might indeed be successful. %K Computer Science, Computational Complexity, cs.CC,Mathematics, Algebraic Geometry, math.AG,Mathematics, Representation Theory, math.RT

%0 Journal Article %A Boczkowski, Lucas %A Korman, Amos %A Natale, Emanuele %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B2F2-2 %R 10.1007/s00446-018-0330-x %7 2018 %D 2019 %J Distributed Computing %V 32 %N 3 %& 173 %P 173 - 191 %I Springer International %C Berlin %@ false

%0 Journal Article %A Borassi, Michele %A Natale, Emanuele %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T KADABRA is an ADaptive Algorithm for Betweenness via Random Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0003-7A10-2 %R 10.1145/3284359 %7 2019 %D 2019 %J Journal of Experimental Algorithmics %V 24 %N 1 %Z sequence number: 1.2 %I ACM %C New York, NY %@ false

%0 Journal Article %A Bressan, Marco %A Leucci, Stefano %A Panconesi, Alessandro %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Motivo: Fast Motif Counting via Succinct Color Coding and Adaptive Sampling : %G eng %U http://hdl.handle.net/21.11116/0000-0005-6A05-F %R 10.14778/3342263.3342640 %7 2019 %D 2019 %J Proccedings of the VLDB Endowment %V 12 %N 11 %& 1651 %P 1651 - 1663 %I ACM %C New York, NY %@ false

%0 Journal Article %A Bringmann, Karl %A Grandoni, Fabrizio %A Saha, Barna %A Vassilevska Williams, Virginia %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Truly Subcubic Algorithms for Language Edit Distance and RNA Folding via Fast Bounded-Difference Min-Plus Product : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7E4-F %R 10.1137/17M112720X %7 2019 %D 2019 %J SIAM Journal on Computing %V 48 %N 2 %& 481 %P 481 - 512 %I SIAM %C Philadelphia, PA %@ false

%0 Conference Proceedings %A Bringmann, Karl %A Kisfaludi-Bak, S&#225;ndor %A Pilipczuk, Michal %A van Leeuwen, Erik Jan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T On Geometric Set Cover for Orthants : %G eng %U http://hdl.handle.net/21.11116/0000-0005-2040-E %R 10.4230/LIPIcs.ESA.2019.26 %U urn:nbn:de:0030-drops-111476 %D 2019 %B 27th Annual European Symposium on Algorithms %Z date of event: 2019-09-09 - 2019-09-11 %C Munich/Garching, Germany %B 27th Annual European Symposium on Algorithms %E Bender, Michael A.; Svensson, Ola; German, Grzegorz %P 1 - 18 %Z sequence number: 26 %I Schloss Dagstuhl %@ 978-3-95977-124-5 %B Leibniz International Proceedings in Informatics %N 144 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/11147/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Bringmann, Karl %A Husfeldt, Thore %A Magnusson, M&#229;ns %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9CFE-1 %R 10.4230/LIPIcs.IPEC.2018.4 %U urn:nbn:de:0030-drops-102050 %D 2019 %B 13th International Symposium on Parameterized and Exact Computation %Z date of event: 2018-08-20 - 2018-08-24 %C Helsinki, Finland %B 13th International Symposium on Parameterized and Exact Computation %E Paul, Christophe; Pilipczuk, Michal %P 1 - 13 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-084-2 %B Leibniz International Proceedings in Informatics %N 115 %U http://drops.dagstuhl.de/opus/volltexte/2019/10205/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Journal Article %A Bringmann, Karl %A Keusch, Ralph %A Lengler, Johannes %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Geometric Inhomogeneous Random Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0B00-1 %R 10.1016/j.tcs.2018.08.014 %7 2018 %D 2019 %J Theoretical Computer Science %V 760 %& 35 %P 35 - 54 %I Elsevier %C Amsterdam %@ false

%0 Conference Proceedings %A Bringmann, Karl %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity Theory (Tutorial) : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B36E-8 %R 10.4230/LIPIcs.STACS.2019.4 %D 2019 %B 36th Symposium on Theoretical Aspects of Computer Science %Z date of event: 2019-03-13 - 2019-03-16 %C Berlin, Germany %B 36th Symposium on Theoretical Aspects of Computer Science %E Niedermeier, Rolf; Paul, Christophe %P 1 - 7 %Z sequence number: 4 %I Schloss Dagstuhl %@ 978-3-95977-100-9 %B Leibniz International Proceedings in Informatics %N 126 %U http://drops.dagstuhl.de/opus/volltexte/2019/10243/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A W&#281;grzycki, Karol %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max : %G eng %U http://hdl.handle.net/21.11116/0000-0002-FC7A-A %R 10.1145/3313276.3316373 %D 2019 %B 51st Annual ACM Symposium on the Theory of Computing %Z date of event: 2019-06-23 - 2019-06-26 %C Phoenix, AZ, USA %B STOC'19 %E Charikar, Moses; Cohen, Edith %P 943 - 954 %I ACM %@ 978-1-4503-6705-9

%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A W&#281;grzycki, Karol %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Approximating APSP without Scaling: Equivalence of Approximate Min-Plus and Exact Min-Max : %G eng %U http://hdl.handle.net/21.11116/0000-0005-3D73-6 %U http://arxiv.org/abs/1907.11078 %D 2019 %X Zwick's $(1+\varepsilon)$-approximation algorithm for the All Pairs Shortest Path (APSP) problem runs in time $\widetilde{O}(\frac{n^\omega}{\varepsilon} \log{W})$, where $\omega \le 2.373$ is the exponent of matrix multiplication and $W$ denotes the largest weight. This can be used to approximate several graph characteristics including the diameter, radius, median, minimum-weight triangle, and minimum-weight cycle in the same time bound. Since Zwick's algorithm uses the scaling technique, it has a factor $\log W$ in the running time. In this paper, we study whether APSP and related problems admit approximation schemes avoiding the scaling technique. That is, the number of arithmetic operations should be independent of $W$; this is called strongly polynomial. Our main results are as follows. - We design approximation schemes in strongly polynomial time $O(\frac{n^\omega}{\varepsilon} \text{polylog}(\frac{n}{\varepsilon}))$ for APSP on undirected graphs as well as for the graph characteristics diameter, radius, median, minimum-weight triangle, and minimum-weight cycle on directed or undirected graphs. - For APSP on directed graphs we design an approximation scheme in strongly polynomial time $O(n^{\frac{\omega + 3}{2}} \varepsilon^{-1} \text{polylog}(\frac{n}{\varepsilon}))$. This is significantly faster than the best exact algorithm. - We explain why our approximation scheme for APSP on directed graphs has a worse exponent than $\omega$: Any improvement over our exponent $\frac{\omega + 3}{2}$ would improve the best known algorithm for Min-Max Product In fact, we prove that approximating directed APSP and exactly computing the Min-Max Product are equivalent. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC

%0 Conference Proceedings %A Bringmann, Karl %A Fischer, Nick %A K&#252;nnemann, Marvin %+ 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 Fine-Grained Analogue of Schaefer's Theorem in P: Dichotomy of &#8707;k&#8704;-Quantified First-Order Graph Properties : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1FAF-5 %R 10.4230/LIPIcs.CCC.2019.31 %U urn:nbn:de:0030-drops-108533 %D 2019 %B 34th Computational Complexity Conference %Z date of event: 2019-07-18 - 2019-07-20 %C New Brunswick, NJ, USA %B 34th Computational Complexity Conference %E Shpilka, Amir %P 1 - 27 %Z sequence number: 31 %I Schloss Dagstuhl %@ 978-3-95977-116-0 %B Leibniz International Proceedings in Informatics %N 137 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10853/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Wellnitz, Philip %+ 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 Few Matches or Almost Periodicity: Faster Pattern Matching with Mismatches in Compressed Texts : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E1F-B %R 10.1137/1.9781611975482.69 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 1126 - 1145 %I SIAM %@ 978-1-61197-548-2

%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ 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 Walking the Dog Fast in Practice: Algorithm Engineering of the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-0005-3D76-3 %U http://arxiv.org/abs/1901.01504 %D 2019 %X The Fr\'echet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Fr\'echet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Fr\'echet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Fr\'echet distance. In this work, we present a fast, certifying implementation for deciding the Fr\'echet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure. %K Computer Science, Computational Geometry, cs.CG

%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ 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 Walking the Dog Fast in Practice: Algorithm Engineering of the Fr&#233;chet Distance : %G eng %U http://hdl.handle.net/21.11116/0000-0003-65C1-1 %R 10.4230/LIPIcs.SoCG.2019.17 %U urn:nbn:de:0030-drops-104219 %D 2019 %B 35th International Symposium on Computational Geometry %Z date of event: 2019-06-18 - 2019-06-21 %C Portland, OR, USA %B 35th International Symposium on Computational Geometry %E Barequet, Gill; Wang, Yusu %P 1 - 21 %Z sequence number: 17 %I Schloss Dagstuhl %@ 978-3-95977-104-7 %B Leibniz International Proceedings in Informatics %N 129 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10421/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ 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 Fr&#233;chet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E29-F %R 10.1137/1.9781611975482.180 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 2902 - 2921 %I SIAM %@ 978-1-61197-548-2

%0 Conference Proceedings %A Bringmann, Karl %A Ray Chaudhury, Bhaskar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Polyline Simplification has Cubic Complexity : %G eng %U http://hdl.handle.net/21.11116/0000-0003-65C8-A %R 10.4230/LIPIcs.SoCG.2019.18 %U urn:nbn:de:0030-drops-104224 %D 2019 %B 35th International Symposium on Computational Geometry %Z date of event: 2019-06-18 - 2019-06-21 %C Portland, OR, USA %B 35th International Symposium on Computational Geometry %E Barequet, Gill; Wang, Yusu %P 1 - 16 %Z sequence number: 18 %I Schloss Dagstuhl %@ 978-3-95977-104-7 %B Leibniz International Proceedings in Informatics %N 129 %U http://drops.dagstuhl.de/opus/volltexte/2019/10422/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Buchin, Kevin %A Driemel, Anne %A van de L'Isle, Natasja %A Nusser, Andr&#233; %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T klcluster: Center-based Clustering of Trajectories : %G eng %U http://hdl.handle.net/21.11116/0000-0005-8705-D %R 10.1145/3347146.3359111 %D 2019 %B 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems %Z date of event: 2019-11-05 - 2019-11-08 %C Chicago, IL, USA %B 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems %E Banaei-Kashani, Farnoush; Trajcevski, Goce; G&#252;ting, Ralf Hartmut; Kulik, Lars; Newsam, Shawn %P 496 - 499 %I ACM %@ 978-1-4503-6909-1

%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-Containing Sorting via Parallel Prefix Computation : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1C6B-5 %U http://arxiv.org/abs/1911.00267 %D 2019 %X Friedrichs et al. (TC 2018) showed that metastability can be contained when sorting inputs arising from time-to-digital converters, i.e., measurement values can be correctly sorted without resolving metastability using synchronizers first. However, this work left open whether this can be done by small circuits. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Our solution utilizes the parallel prefix computation (PPC) framework (JACM 1980). We improve this construction by bounding its fan-out by an arbitrary $f \geq 3$, without affecting depth and increasing circuit size by a small constant factor only. Thus, we obtain the first PPC circuits with asymptotically optimal size, constant fan-out, and optimal depth. To show that applying the PPC framework to the sorting task is feasible, we prove that the latter can, despite potential metastability, be decomposed such that the core operation is associative. We obtain asymptotically optimal metastability-containing sorting networks. We complement these results with simulations, independently verifying the correctness as well as small size and delay of our circuits. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Architecture, cs.AR

%0 Conference Proceedings %A Bund, Johannes %A Lenzen, Christoph %A Rosenbaum, Will %+ 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 Fault Tolerant Gradient Clock Synchronization : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1BE3-D %R 10.1145/3293611.3331637 %D 2019 %B ACM Symposium on Principles of Distributed Computing %Z date of event: 2019-07-29 - 2019-08-02 %C Toronto, Canada %B PODC'19 %P 357 - 365 %I ACM %@ 978-1-4503-6217-7

%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Rosenbaum, Will %+ 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 Fault Tolerant Gradient Clock Synchronization : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0CD6-F %U http://arxiv.org/abs/1902.08042 %D 2019 %X Synchronizing clocks in distributed systems is well-understood, both in terms of fault-tolerance in fully connected systems and the dependence of local and global worst-case skews (i.e., maximum clock difference between neighbors and arbitrary pairs of nodes, respectively) on the diameter of fault-free systems. However, so far nothing non-trivial is known about the local skew that can be achieved in topologies that are not fully connected even under a single Byzantine fault. Put simply, in this work we show that the most powerful known techniques for fault-tolerant and gradient clock synchronization are compatible, in the sense that the best of both worlds can be achieved simultaneously. Concretely, we combine the Lynch-Welch algorithm [Welch1988] for synchronizing a clique of $n$ nodes despite up to $f<n/3$ Byzantine faults with the gradient clock synchronization (GCS) algorithm by Lenzen et al. [Lenzen2010] in order to render the latter resilient to faults. As this is not possible on general graphs, we augment an input graph $\mathcal{G}$ by replacing each node by $3f+1$ fully connected copies, which execute an instance of the Lynch-Welch algorithm. We then interpret these clusters as supernodes executing the GCS algorithm, where for each cluster its correct nodes' Lynch-Welch clocks provide estimates of the logical clock of the supernode in the GCS algorithm. By connecting clusters corresponding to neighbors in $\mathcal{G}$ in a fully bipartite manner, supernodes can inform each other about (estimates of) their logical clock values. This way, we achieve asymptotically optimal local skew, granted that no cluster contains more than $f$ faulty nodes, at factor $O(f)$ and $O(f^2)$ overheads in terms of nodes and edges, respectively. Note that tolerating $f$ faulty neighbors trivially requires degree larger than $f$, so this is asymptotically optimal as well. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC,Computer Science, Data Structures and Algorithms, cs.DS

%0 Journal Article %A B&#252;rgisser, Peter %A Ikenmeyer, Christian %A Panova, Greta %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T No Occurrence Obstructions in Geometric Complexity Theory : %G eng %U http://hdl.handle.net/21.11116/0000-0002-72B9-D %R 10.1090/jams/908 %7 2018 %D 2019 %J Journal of the American Mathematical Society %O J. Amer. Math. Soc. %V 32 %& 163 %P 163 - 193 %I The Society %C Providence, R.I. %@ false

%0 Conference Proceedings %A Chalermsook, Parinya %A Schmid, Andreas %A Uniyal, Sumedha %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Tight Extremal Bound on the Lov&#225;sz Cactus Number in Planar Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5D6-A %R 10.4230/LIPIcs.STACS.2019.19 %D 2019 %B 36th Symposium on Theoretical Aspects of Computer Science %Z date of event: 2019-03-13 - 2019-03-16 %C Berlin, Germany %B 36th Symposium on Theoretical Aspects of Computer Science %E Niedermeier, Rolf; Paul, Christophe %P 1 - 14 %Z sequence number: 19 %I Schloss Dagstuhl %@ 978-3-95977-100-9 %B Leibniz International Proceedings in Informatics %N 126 %U http://drops.dagstuhl.de/doku/urheberrecht1.htmlhttp://drops.dagstuhl.de/opus/volltexte/2019/10258/

%0 Journal Article %A Chandran, L. Sunil %A Issac, Davis %A Zhou, Sanming %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Hadwiger's Conjecture for Squares of 2-Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E5B-7 %R 10.1016/j.ejc.2018.10.003 %7 2018 %D 2019 %J European Journal of Combinatorics %V 76 %& 159 %P 159 - 174 %I Elsevier %C Amsterdam %@ false

%0 Conference Proceedings %A Chen, Lin %A Eberle, Franziska %A Megow, Nicole %A Schewior, Kevin %A Stein, Clifford %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A General Framework for Handling Commitment in Online Admission Control : %G eng %U http://hdl.handle.net/21.11116/0000-0002-F4CC-5 %D 2019 %B 20th Conference on Integer Programming and Combinatorial Optimization %Z date of event: 2019-05-22 - 2019-05-24 %C Ann Arbor, MI, USA %B Integer Programming and Combinatorial Optimization %I Springer

%0 Journal Article %A Chen, Ning %A Hoefer, Martin %A K&#252;nnemann, Marvin %A Lin, Chengyu %A Miao, Peihan %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Secretary Markets with Local Information : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A90C-3 %R 10.1007/s00446-018-0327-5 %7 2019 %D 2019 %J Distributed Computing %V 32 %N 5 %& 361 %P 361 - 378 %I Springer International %C Berlin %@ false

%0 Conference Proceedings %A Cheung, Yun Kuen %A Hoefer, Martin %A Nakhe, Paresh %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Tracing Equilibrium in Dynamic Markets via Distributed Adaptation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5FE-E %U http://dl.acm.org/citation.cfm?id=3306127.3331825 %D 2019 %B 18th International Conference on Autonomous Agents and Multiagent Systems %Z date of event: 2019-05-13 - 2019-05-17 %C Montreal, Canada %B AAMAS'19 %P 1225 - 1233 %I ACM %@ 978-1-4503-6309-9

%0 Journal Article %A Chiantini, Luca %A Ikenmeyer, Christian %A Landsberg, J. M. %A Ottaviani, Giorgio %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The Geometry of Rank Decompositions of Matrix Multiplication I: 2x2 Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AB12-9 %R 10.1080/10586458.2017.1403981 %7 2017 %D 2019 %J Experimental Mathematics %V 28 %N 3 %& 322 %P 322 - 327 %I Taylor & Francis %C Boston, MA %@ false

%0 Journal Article %A Choudhary, Aruni %A Kerber, Michael %A Raghvendra, Sharat %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Polynomial-Sized Topological Approximations Using the Permutahedron : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5B6-E %R 10.1007/s00454-017-9951-2 %7 2017 %D 2019 %J Discrete & Computational Geometry %V 61 %N 1 %& 42 %P 42 - 80 %I Springer %C New York, NY %@ false

%0 Conference Proceedings %A Choudhary, Aruni %A Kerber, Michael %A Raghvendra, Sharath %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Improved Topological Approximations by Digitization : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5BC-8 %R 10.1137/1.9781611975482.166 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 2675 - 2688 %I SIAM %@ 978-1-61197-548-2

%0 Journal Article %A Choudhary, Aruni %A Ghosh, Arijit %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Delaunay Simplices in Diagonally Distorted Lattices : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5C1-1 %D 2019 %J Computational Geometry: Theory and Applications %I Elsevier %C Amsterdam %@ false

%0 Journal Article %A Christodoulou, George %A Sgouritsa, Alkmini %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Designing Networks with Good Equilibria under Uncertainty : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AEC7-A %R 10.1137/16M1096694 %7 2019 %D 2019 %J SIAM Journal on Computing %V 48 %N 4 %& 1364 %P 1364 - 1396 %I SIAM %C Philadelphia, PA %@ false

%0 Journal Article %A Correa, Jos&#233; %A Foncea, Patricio %A Hoeksma, Ruben %A Oosterwijk, Tim %A Vredeveld, Tjark %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Recent Developments in Prophet Inequalities : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E6F-1 %7 2019 %D 2019 %J ACM SIGecom Exchanges %V 17 %N 1 %& 60 %P 60 - 61 %I ACM %C New York, NY %@ false %U http://www.sigecom.org/exchanges/volume_17/1/CORREA.pdf

%0 Conference Proceedings %A Cruciani, Emilio %A Natale, Emanuele %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Distributed Community Detection via Metastability of the 2-Choices Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A985-9 %R 10.1609/aaai.v33i01.33016046 %D 2019 %B Thirty-Third AAAI Conference on Artificial Intelligence %Z date of event: 2019-01-27 - 2019-02-01 %C Honolulu, HI, USA %B Thirty-Third AAAI Conference on Artificial Intelligence %P 6046 - 6053 %I AAAI %@ 978-1-57735-809-1

%0 Journal Article %A Daescu, Ovidiu %A Friedrichs, Stephan %A Malik, Hemant %A Polishchuk, Valentin %A Schmidt, Christiane %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Altitude Terrain Guarding and Guarding Uni-monotone Polygons : %G eng %U http://hdl.handle.net/21.11116/0000-0004-E572-9 %R 10.1016/j.comgeo.2019.07.004 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 84 %& 22 %P 22 - 35 %I Elsevier %C Amsterdam %@ false

%0 Conference Proceedings %A Dell, Holger %A Roth, Marc %A Wellnitz, Philip %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Answers to Existential Questions : %G eng %U http://hdl.handle.net/21.11116/0000-0005-8653-6 %R 10.4230/LIPIcs.ICALP.2019.113 %U urn:nbn:de:0030-drops-106894 %D 2019 %B 46th International Colloquium on Automata, Languages, and Programming %Z date of event: 2019-07-09 - 2019-07-12 %C Patras, Greece %B 46th International Colloquium on Automata, Languages, and Programming %E Baier, Christel; Chaztigiannakis, Ioannis; Flocchini, Paola; Leonardi, Stefano %Z sequence number: 113 %I Schloss Dagstuhl %@ 978-3-95977-109-2 %B Leibniz International Proceedings in Informatics %N 132 %U https://doi.org/10.4230/LIPIcs.ICALP.2019.113https://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A D&#246;rfler, Julian %A Roth, Marc %A Schmitt, Johannes %A Wellnitz, Philip %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Counting Induced Subgraphs: An Algebraic Approach to #W[1]-hardness : %G eng %U http://hdl.handle.net/21.11116/0000-0005-85DB-E %R 10.4230/LIPIcs.MFCS.2019.26 %U urn:nbn:de:0030-drops-109703 %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: 26 %I Schloss Dagstuhl %@ 978-3-95977-117-7 %B Leibniz International Proceedings in Informatics %N 138 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2019/10970/https://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Report %A D&#246;rfler, Julian %A Ikenmeyer, Christian %A Panova, Greta %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Geometric Complexity Theory: Multiplicity Obstructions are Stronger than Occurrence Obstructions : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B393-C %U http://arxiv.org/abs/1901.04576 %D 2019 %X Geometric Complexity Theory as initiated by Mulmuley and Sohoni in two papers (SIAM J Comput 2001, 2008) aims to separate algebraic complexity classes via representation theoretic multiplicities in coordinate rings of specific group varieties. The papers also conjecture that the vanishing behavior of these multiplicities would be sufficient to separate complexity classes (so-called occurrence obstructions). The existence of such strong occurrence obstructions has been recently disproven in 2016 in two successive papers, Ikenmeyer-Panova (Adv. Math.) and B\"urgisser-Ikenmeyer-Panova (J. AMS). This raises the question whether separating group varieties via representation theoretic multiplicities is stronger than separating them via occurrences. This paper provides for the first time a setting where separating with multiplicities can be achieved, while the separation with occurrences is provably impossible. Our setting is surprisingly simple and natural: We study the variety of products of homogeneous linear forms (the so-called Chow variety) and the variety of polynomials of bounded border Waring rank (i.e. a higher secant variety of the Veronese variety). As a side result we prove a slight generalization of Hermite's reciprocity theorem, which proves Foulkes' conjecture for a new infinite family of cases. %K Computer Science, Computational Complexity, cs.CC,Mathematics, Algebraic Geometry, math.AG,Mathematics, Combinatorics, math.CO,Mathematics, Representation Theory, math.RT,

%0 Journal Article %A Duraj, Lech %A K&#252;nnemann, Marvin %A Polak, Adam %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Tight Conditional Lower Bounds for Longest Common Increasing Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A906-9 %R 10.1007/s00453-018-0485-7 %7 2018 %D 2019 %J Algorithmica %V 81 %N 10 %& 3968 %P 3968 - 3992 %I Springer %C New York, NY %@ false

%0 Report %A Eden, Talya %A Ron, Dana %A Rosenbaum, Will %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T The Arboricity Captures the Complexity of Sampling Edges : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0CD0-5 %U http://arxiv.org/abs/1902.08086 %D 2019 %X In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$. Given query access to a graph $G$ over $n$ vertices and of average degree $d$ and arboricity at most $\alpha$, we design an algorithm that performs $O\!\left(\frac{\alpha}{d} \cdot \frac{\log^3 n}{\varepsilon}\right)$ queries in expectation and returns an edge in the graph such that every edge $e \in E$ is sampled with probability $(1 \pm \varepsilon)/m$. The algorithm performs two types of queries: degree queries and neighbor queries. We show that the upper bound is tight (up to poly-logarithmic factors and the dependence in $\varepsilon$), as $\Omega\!\left(\frac{\alpha}{d} \right)$ queries are necessary for the easier task of sampling edges from any distribution over $E$ that is close to uniform in total variational distance. We also prove that even if $G$ is a tree (i.e., $\alpha = 1$ so that $\frac{\alpha}{d}=\Theta(1)$), $\Omega\left(\frac{\log n}{\log\log n}\right)$ queries are necessary to sample an edge from any distribution that is pointwise close to uniform, thus establishing that a $\mathrm{poly}(\log n)$ factor is necessary for constant $\alpha$. Finally we show how our algorithm can be applied to obtain a new result on approximately counting subgraphs, based on the recent work of Assadi, Kapralov, and Khanna (ITCS, 2019). %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS

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

%0 Journal Article %A Fraigniaud, Pierre %A Natale, Emanuele %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Noisy Rumor Spreading and Plurality Consensus : %G eng %U http://hdl.handle.net/21.11116/0000-0002-6CD7-3 %R 10.1007/s00446-018-0335-5 %7 2018 %D 2019 %J Distributed Computing %V 32 %N 4 %& 257 %P 257 - 276 %I Springer International %C Berlin %@ false

%0 Conference Proceedings %A Funke, Stefan %A Rupp, Tobias %A Nusser, Andr&#233; %A Storandt, Sabine %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T PATHFINDER: Storage and Indexing of Massive Trajectory Sets : %G eng %U http://hdl.handle.net/21.11116/0000-0005-870C-6 %R 10.1145/3340964.3340978 %D 2019 %B 16th International Symposium onSpatial and Temporal Databases %Z date of event: 2019-08-19 - 2019-08-21 %C Vienna, Austria %B SSTD'19 %E Aref, Walid G.; Bertolotto, Michela; Bouros, Pnagiotis; Jensen, Christian S.; Mahmood, Ahmed; N&#248;rv&#229;g, Kjetil; Sacharidis, Dimitris; Sarwat, Mohamed %P 90 - 99 %I ACM %@ 978-1-4503-6280-1

%0 Journal Article %A Gonczarowski, Yannai A. %A Nisan, Noam %A Ostrovsky, Rafail %A Rosenbaum, Will %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Stable Marriage Requires Communication : %G eng %U http://hdl.handle.net/21.11116/0000-0005-88FD-5 %R 10.1016/j.geb.2018.10.013 %7 2019 %D 2019 %J Games and Economic Behavior %V 118 %& 626 %P 626 - 646 %I Elsevier %C Amsterdam %@ false

%0 Conference Proceedings %A Grandoni, Fabrizio %A Laekhanukit, Bundit %A Li, Shi %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T O(log 2 k/ log log k)-Approximation Algorithm for Directed Steiner Tree: A Tight Quasi-Polynomial-Time Algorithm : %G eng %U http://hdl.handle.net/21.11116/0000-0003-1625-B %R 10.1145/3313276.3316349 %D 2019 %B 51st Annual ACM Symposium on the Theory of Computing %Z date of event: 2019-06-23 - 2019-06-26 %C Phoenix, AZ, USA %B STOC'19 %P 253 - 264 %I ACM %@ 978-1-4503-6705-9

%0 Journal Article %A Heydrich, Sandy %A Wiese, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Faster Approximation Schemes for the Two-dimensional Knapsack Problem : %G eng %U http://hdl.handle.net/21.11116/0000-0005-6A94-D %R 10.1145/3338512 %7 2019 %D 2019 %J ACM Transactions on Algorithms %V 15 %N 4 %Z sequence number: 47 %I ACM %C New York, NY %@ false

%0 Conference Proceedings %A Ibrahim, Yusra %A Riedewald, Mirek %A Weikum, Gerhard %A Zeinalipour-Yazti, Demetrios %+ Databases and Information Systems, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society Databases and Information Systems, MPI for Informatics, Max Planck Society Databases and Information Systems, MPI for Informatics, Max Planck Society %T Bridging Quantities in Tables and Text : %G eng %U http://hdl.handle.net/21.11116/0000-0003-01AB-B %R 10.1109/ICDE.2019.00094 %D 2019 %B 35th IEEE International Conference on Data Engineering %Z date of event: 2019-04-08 - 2019-04-12 %C Macau, China %B ICDE 2019 %P 1010 - 1021 %I IEEE %@ 978-1-5386-7474-1

%0 Journal Article %A Ikenmeyer, Christian %A Komarath, Balagopal %A Lenzen, Christoph %A Lysikov, Vladimir %A Mokhov, Andrey %A Sreenivasaiah, Karteek %+ 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 On the Complexity of Hazard-free Circuits : %G eng %U http://hdl.handle.net/21.11116/0000-0004-8D51-2 %R 10.1145/3320123 %7 2019 %D 2019 %J Journal of the ACM %V 66 %N 4 %Z sequence number: 25 %I ACM %C New York, NY %@ false

%0 Thesis %A Issac, Davis %Y Karrenbauer, Andreas %A referee: Mehlhorn, Kurt %A referee: Chandran, L. Sunil %+ Algorithms and Complexity, 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 %T On some covering, partition and connectivity problems in graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0004-D665-9 %R 10.22028/D291-29620 %I Universit&#228;t des Saarlandes %C Saarbr&#252;cken %D 2019 %P 191 p. %V phd %9 phd %X We look at some graph problems related to covering, partition, and connectivity. First, we study the problems of covering and partitioning edges with bicliques, especially from the viewpoint of parameterized complexity. For the partition problem, we develop much more efficient algorithms than the ones previously known. In contrast, for the cover problem, our lower bounds show that the known algorithms are probably optimal. Next, we move on to graph coloring, which is probably the most extensively studied partition problem in graphs. Hadwiger&#8217;s conjecture is a long-standing open problem related to vertex coloring. We prove the conjecture for a special class of graphs, namely squares of 2-trees, and show that square graphs are important in connection with Hadwiger&#8217;s conjecture. Then, we study a coloring problem that has been emerging recently, called rainbow coloring. This problem lies in the intersection of coloring and connectivity. We study different variants of rainbow coloring and present bounds and complexity results on them. Finally, we move on to another parameter related to connectivity called spanning tree congestion (STC). We give tight bounds for STC in general graphs and random graphs. While proving the results on %U https://publikationen.sulb.uni-saarland.de/handle/20.500.11880/28007

%0 Conference Proceedings %A Jindal, Gorav %A Bl&#228;ser, Markus %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Complexity of Symmetric Polynomials : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ABCC-8 %R 10.4230/LIPIcs.ITCS.2019.47 %U urn:nbn:de:0030-drops-101402 %D 2019 %B 10th Innovations in Theoretical Computer Science %Z date of event: 2019-01-10 - 2019-01-12 %C San Diego, CA, USA %B 10th Innovations in Theoretical Computer Science %E Blum, Avrim %P 1 - 14 %Z sequence number: 47 %I Schloss Dagstuhl %@ 978-3-95977-095-8 %B Leibniz International Proceedings in Informatics %N 124 %U http://drops.dagstuhl.de/opus/volltexte/2018/10140/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A John, Maximilian %A Karrenbauer, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Dynamic Sparsification for Quadratic Assignment Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0005-1DA8-E %R 10.1007/978-3-030-22629-9_17 %D 2019 %B 18th International Conference on Mathematical Optimization Theory and Operations Research %Z date of event: 2019-07-08 - 2019-07-12 %C Ekaterinburg, Russia %B Mathematical Optimization Theory and Operations Research %E Khachay, Michael; Kochetov, Yury; Pardalos, Panos %P 232 - 264 %I Springer %B Lecture Notes in Computer Science %N 11548

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

%0 Journal Article %A Khanchandani, Pankaj %A Lenzen, Christoph %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Self-Stabilizing Byzantine Clock Synchronization with Optimal Precision : %G eng %U http://hdl.handle.net/21.11116/0000-0000-73AC-D %R 10.1007/s00224-017-9840-3 %7 2018-01-20 %D 2019 %J Theory of Computing Systems %V 63 %N 2 %& 261 %P 261 - 305 %I Springer %C New York, NY %@ false

%0 Conference Proceedings %A Kinali, Attila %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Physical Sine-to-Square Converter Noise Model : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AC39-D %R 10.1109/FCS.2018.8597525 %D 2019 %B IEEE International Frequency Control Symposium %Z date of event: 2018-05-21 - 2018-05-24 %C Olympic Valley, CA, USA %B IEEE International Frequency Control Symposium %P 383 - 388 %I IEEE %@ 978-1-5386-3214-7

%0 Journal Article %A K&#252;nnemann, Marvin %A Moeller, Daniel %A Paturi, Ramamohan %A Schneider, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Subquadratic Algorithms for Succinct Stable Matching : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7E0-3 %R 10.1007/s00453-019-00564-x %7 2019 %D 2019 %J Algorithmica %V 81 %N 7 %& 2991 %P 2991 - 3024 %I Springer %C New York, NY %@ false

%0 Journal Article %A Lenzen, Christoph %A Rybicki, Joel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Self-Stabilising Byzantine Clock Synchronisation is Almost as Easy as Consensus : %G eng %U http://hdl.handle.net/21.11116/0000-0004-7CF6-C %R 10.1145/3339471 %7 2019 %D 2019 %J Journal of the ACM %V 66 %N 5 %Z sequence number: 32 %I ACM %C New York, NY %@ false

%0 Report %A Lenzen, Christoph %A Parter, Merav %A Yogev, Eylon %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Parallel Balanced Allocations: The Heavily Loaded Case : %G eng %U http://hdl.handle.net/21.11116/0000-0003-B3A4-9 %U http://arxiv.org/abs/1904.07532 %D 2019 %X We study parallel algorithms for the classical balls-into-bins problem, in which $m$ balls acting in parallel as separate agents are placed into $n$ bins. Algorithms operate in synchronous rounds, in each of which balls and bins exchange messages once. The goal is to minimize the maximal load over all bins using a small number of rounds and few messages. While the case of $m=n$ balls has been extensively studied, little is known about the heavily loaded case. In this work, we consider parallel algorithms for this somewhat neglected regime of $m\gg n$. The naive solution of allocating each ball to a bin chosen uniformly and independently at random results in maximal load $m/n+\Theta(\sqrt{m/n\cdot \log n})$ (for $m\geq n \log n$) w.h.p. In contrast, for the sequential setting Berenbrink et al (SIAM J. Comput 2006) showed that letting each ball join the least loaded bin of two randomly selected bins reduces the maximal load to $m/n+O(\log\log m)$ w.h.p. To date, no parallel variant of such a result is known. We present a simple parallel threshold algorithm that obtains a maximal load of $m/n+O(1)$ w.h.p. within $O(\log\log (m/n)+\log^* n)$ rounds. The algorithm is symmetric (balls and bins all "look the same"), and balls send $O(1)$ messages in expectation per round. The additive term of $O(\log^* n)$ in the complexity is known to be tight for such algorithms (Lenzen and Wattenhofer Distributed Computing 2016). We also prove that our analysis is tight, i.e., algorithms of the type we provide must run for $\Omega(\min\{\log\log (m/n),n\})$ rounds w.h.p. Finally, we give a simple asymmetric algorithm (i.e., balls are aware of a common labeling of the bins) that achieves a maximal load of $m/n + O(1)$ in a constant number of rounds w.h.p. Again, balls send only a single message per round, and bins receive $(1+o(1))m/n+O(\log n)$ messages w.h.p. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Conference Proceedings %A Lenzen, Christoph %A Parter, Merav %A Yogev, Eylon %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Parallel Balanced Allocations: The Heavily Loaded Case : %G eng %U http://hdl.handle.net/21.11116/0000-0003-6593-5 %R 10.1145/3323165.3323203 %D 2019 %B 31st ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2019-06-22 - 2019-06-24 %C Phoenix, AZ, USA %B SPAA'19 %P 313 - 322 %I ACM %@ 978-1-4503-6184-2

%0 Journal Article %A Lenzen, Christoph %A Rybicki, Joel %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Near-Optimal Self-stabilising Counting and Firing Squads : %G eng %U http://hdl.handle.net/21.11116/0000-0004-7AD6-2 %R 10.1007/s00446-018-0342-6 %7 2018 %D 2019 %J Distributed Computing %V 32 %N 4 %& 339 %P 339 - 360 %I Springer International %C Berlin %@ false

%0 Journal Article %A Lenzen, Christoph %A Patt-Shamir, Boaz %A Peleg, David %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Distributed Distance Computation and Routing with Small Messages : %G eng %U http://hdl.handle.net/21.11116/0000-0002-6CD1-9 %R 10.1007/s00446-018-0326-6 %7 2018 %D 2019 %J Distributed Computing %V 32 %N 2 %& 133 %P 133 - 157 %I Springer International %C Berlin %@ false

%0 Report %A Miller, Avery %A Patt-Shamir, Boaz %A Rosenbaum, Will %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T With Great Speed Come Small Buffers: Space-Bandwidth Tradeoffs for Routing : %G eng %U http://hdl.handle.net/21.11116/0000-0003-0CD3-2 %U http://arxiv.org/abs/1902.08069 %D 2019 %X We consider the Adversarial Queuing Theory (AQT) model, where packet arrivals are subject to a maximum average rate $0\le\rho\le1$ and burstiness $\sigma\ge0$. In this model, we analyze the size of buffers required to avoid overflows in the basic case of a path. Our main results characterize the space required by the average rate and the number of distinct destinations: we show that $O(k d^{1/k})$ space suffice, where $d$ is the number of distinct destinations and $k=\lfloor 1/\rho \rfloor$; and we show that $\Omega(\frac 1 k d^{1/k})$ space is necessary. For directed trees, we describe an algorithm whose buffer space requirement is at most $1 + d' + \sigma$ where $d'$ is the maximum number of destinations on any root-leaf path. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Conference Proceedings %A Oh, Eunjin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Optimal Algorithm for Geodesic Nearest-point Voronoi Diagrams in Simple Polygons : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AA78-8 %R 10.1137/1.9781611975482.25 %D 2019 %B 30th Annual ACM-SIAM Symposium on Discrete Algorithms %Z date of event: 2019-01-06 - 2019-01-09 %C San Diego, CA, USA %B Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms %E Chan, Timothy M. %P 391 - 409 %I SIAM %@ 978-1-61197-548-2

%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Computing the Center Region and its Variants : %G eng %U http://hdl.handle.net/21.11116/0000-0004-E587-1 %R 10.1016/j.tcs.2018.06.026 %7 2019 %D 2019 %J Theoretical Computer Science %V 789 %& 2 %P 2 - 12 %I Elsevier %C Amsterdam %@ false

%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A New Balanced Subdivision of a Simple Polygon for Time-Space Trade-Off Algorithms : %G eng %U http://hdl.handle.net/21.11116/0000-0003-A7DE-7 %R 10.1007/s00453-019-00558-9 %7 2019 %D 2019 %J Algorithmica %V 81 %N 7 %& 2829 %P 2829 - 2856 %I Springer %C New York, NY %@ false

%0 Journal Article %A Oh, Eunjin %A Ahn, Hee-Kap %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Assigning Weights to Minimize the Covering Radius in the Plane : %G eng %U http://hdl.handle.net/21.11116/0000-0003-C34C-C %R 10.1016/j.comgeo.2018.10.007 %7 2019 %D 2019 %J Computational Geometry: Theory and Applications %V 81 %& 22 %P 22 - 32 %I Elsevier %C Amsterdam %@ false

%0 Conference Proceedings %A Patt-Shamir, Boaz %A Rosenbaum, Will %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Space-Optimal Packet Routing on Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0004-AAD1-0 %R 10.1109/INFOCOM.2019.8737596 %D 2019 %B IEEE Conference on Computer Communications %Z date of event: 2019-04-29 - 2019-05-02 %C Paris, France %B IEEE Conference on Computer Communications %P 1036 - 1044 %I IEEE %@ 978-1-7281-0515-4

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

%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.

%0 Journal Article %A Schroeder, Pascal %A Kacem, Imed %A Schmidt, G&#252;nter %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Optimal Online Algorithms for the Portfolio Selection Problem, Bi-Directional Trading and -Search with Interrelated Prices : %G eng %U http://hdl.handle.net/21.11116/0000-0004-7AEC-A %R 10.1051/ro/2018064 %7 2019 %D 2019 %J RAIRO - Operations Research %V 53 %N 2 %& 559 %P 559 - 576 %I EDP Sciences %C Les Ulis, France %@ false

%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tighter Connections Between Formula-SAT and Shaving Logs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-16FB-B %R 10.4230/LIPIcs.ICALP.2018.8 %U urn:nbn:de:0030-drops-90129 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 18 %Z sequence number: 8 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9012/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Report %A Abboud, Amir %A Bringmann, Karl %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Tighter Connections Between Formula-SAT and Shaving Logs : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3DF7-5 %U http://arxiv.org/abs/1804.08978 %D 2018 %X A noticeable fraction of Algorithms papers in the last few decades improve the running time of well-known algorithms for fundamental problems by logarithmic factors. For example, the $O(n^2)$ dynamic programming solution to the Longest Common Subsequence problem (LCS) was improved to $O(n^2/\log^2 n)$ in several ways and using a variety of ingenious tricks. This line of research, also known as "the art of shaving log factors", lacks a tool for proving negative results. Specifically, how can we show that it is unlikely that LCS can be solved in time $O(n^2/\log^3 n)$? Perhaps the only approach for such results was suggested in a recent paper of Abboud, Hansen, Vassilevska W. and Williams (STOC'16). The authors blame the hardness of shaving logs on the hardness of solving satisfiability on Boolean formulas (Formula-SAT) faster than exhaustive search. They show that an $O(n^2/\log^{1000} n)$ algorithm for LCS would imply a major advance in circuit lower bounds. Whether this approach can lead to tighter barriers was unclear. In this paper, we push this approach to its limit and, in particular, prove that a well-known barrier from complexity theory stands in the way for shaving five additional log factors for fundamental combinatorial problems. For LCS, regular expression pattern matching, as well as the Fr\'echet distance problem from Computational Geometry, we show that an $O(n^2/\log^{7+\varepsilon} n)$ runtime would imply new Formula-SAT algorithms. Our main result is a reduction from SAT on formulas of size $s$ over $n$ variables to LCS on sequences of length $N=2^{n/2} \cdot s^{1+o(1)}$. Our reduction is essentially as efficient as possible, and it greatly improves the previously known reduction for LCS with $N=2^{n/2} \cdot s^c$, for some $c \geq 100$. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS

%0 Report %A Abboud, Amir %A Bringmann, Karl %A Hermelin, Danny %A Shabtay, Dvir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T SETH-Based Lower Bounds for Subset Sum and Bicriteria Path : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E17-3 %U http://arxiv.org/abs/1704.04546 %D 2018 %X Subset-Sum and k-SAT are two of the most extensively studied problems in computer science, and conjectures about their hardness are among the cornerstones of fine-grained complexity. One of the most intriguing open problems in this area is to base the hardness of one of these problems on the other. Our main result is a tight reduction from k-SAT to Subset-Sum on dense instances, proving that Bellman's 1962 pseudo-polynomial $O^{*}(T)$-time algorithm for Subset-Sum on $n$ numbers and target $T$ cannot be improved to time $T^{1-\varepsilon}\cdot 2^{o(n)}$ for any $\varepsilon>0$, unless the Strong Exponential Time Hypothesis (SETH) fails. This is one of the strongest known connections between any two of the core problems of fine-grained complexity. As a corollary, we prove a "Direct-OR" theorem for Subset-Sum under SETH, offering a new tool for proving conditional lower bounds: It is now possible to assume that deciding whether one out of $N$ given instances of Subset-Sum is a YES instance requires time $(N T)^{1-o(1)}$. As an application of this corollary, we prove a tight SETH-based lower bound for the classical Bicriteria s,t-Path problem, which is extensively studied in Operations Research. We separate its complexity from that of Subset-Sum: On graphs with $m$ edges and edge lengths bounded by $L$, we show that the $O(Lm)$ pseudo-polynomial time algorithm by Joksch from 1966 cannot be improved to $\tilde{O}(L+m)$, in contrast to a recent improvement for Subset Sum (Bringmann, SODA 2017). %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC

%0 Conference Proceedings %A Abboud, Amir %A Bringmann, Karl %A Dell, Holger %A Nederlof, Jesper %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T More Consequences of Falsifying SETH and the Orthogonal Vectors Conjecture : %G eng %U http://hdl.handle.net/21.11116/0000-0002-1707-D %R 10.1145/3188745.3188938 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 253 - 266 %I ACM %@ 978-1-4503-5559-9

%0 Report %A Abboud, Amir %A Backurs, Arturs %A Bringmann, Karl %A K&#252;nnemann, Marvin %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Fine-Grained Complexity of Analyzing Compressed Data: Quantifying Improvements over Decompress-And-Solve : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E38-C %U http://arxiv.org/abs/1803.00796 %D 2018 %X Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given a compression of size $n$ of data that originally has size $N$, and we want to solve a problem with time complexity $T(\cdot)$. The naive strategy of "decompress-and-solve" gives time $T(N)$, whereas "the gold standard" is time $T(n)$: to analyze the compression as efficiently as if the original data was small. We restrict our attention to data in the form of a string (text, files, genomes, etc.) and study the most ubiquitous tasks. While the challenge might seem to depend heavily on the specific compression scheme, most methods of practical relevance (Lempel-Ziv-family, dictionary methods, and others) can be unified under the elegant notion of Grammar Compressions. A vast literature, across many disciplines, established this as an influential notion for Algorithm design. We introduce a framework for proving (conditional) lower bounds in this field, allowing us to assess whether decompress-and-solve can be improved, and by how much. Our main results are: - The $O(nN\sqrt{\log{N/n}})$ bound for LCS and the $O(\min\{N \log N, nM\})$ bound for Pattern Matching with Wildcards are optimal up to $N^{o(1)}$ factors, under the Strong Exponential Time Hypothesis. (Here, $M$ denotes the uncompressed length of the compressed pattern.) - Decompress-and-solve is essentially optimal for Context-Free Grammar Parsing and RNA Folding, under the $k$-Clique conjecture. - We give an algorithm showing that decompress-and-solve is not optimal for Disjointness. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS

%0 Conference Proceedings %A Abrahamsen, Mikkel %A Adamaszek, Anna %A Bringmann, Karl %A Cohen-Addad, Vincent %A Mehr, Mehran %A Rotenberg, Eva %A Roytman, Alan %A Thorup, Mikkel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Fast Fencing : %G eng %U http://hdl.handle.net/21.11116/0000-0002-171F-3 %R 10.1145/3188745.3188878 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 564 - 573 %I ACM %@ 978-1-4503-5559-9

%0 Report %A Abrahamsen, Mikkel %A Adamaszek, Anna %A Bringmann, Karl %A Cohen-Addad, Vincent %A Mehr, Mehran %A Rotenberg, Eva %A Roytman, Alan %A Thorup, Mikkel %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations External Organizations External Organizations %T Fast Fencing : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3DFE-E %U http://arxiv.org/abs/1804.00101 %D 2018 %X We consider very natural "fence enclosure" problems studied by Capoyleas, Rote, and Woeginger and Arkin, Khuller, and Mitchell in the early 90s. Given a set $S$ of $n$ points in the plane, we aim at finding a set of closed curves such that (1) each point is enclosed by a curve and (2) the total length of the curves is minimized. We consider two main variants. In the first variant, we pay a unit cost per curve in addition to the total length of the curves. An equivalent formulation of this version is that we have to enclose $n$ unit disks, paying only the total length of the enclosing curves. In the other variant, we are allowed to use at most $k$ closed curves and pay no cost per curve. For the variant with at most $k$ closed curves, we present an algorithm that is polynomial in both $n$ and $k$. For the variant with unit cost per curve, or unit disks, we present a near-linear time algorithm. Capoyleas, Rote, and Woeginger solved the problem with at most $k$ curves in $n^{O(k)}$ time. Arkin, Khuller, and Mitchell used this to solve the unit cost per curve version in exponential time. At the time, they conjectured that the problem with $k$ curves is NP-hard for general $k$. Our polynomial time algorithm refutes this unless P equals NP. %K Computer Science, Computational Geometry, cs.CG

%0 Conference Proceedings %A Adamaszek, Anna %A Antoniadis, Antonios %A Kumar, Amit %A M&#246;mke, Tobias %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Approximating Airports and Railways : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F43-0 %R 10.4230/LIPIcs.STACS.2018.5 %U urn:nbn:de:0030-drops-85183 %D 2018 %B 35th Symposium on Theoretical Aspects of Computer Science %Z date of event: 2018-02-28 - 2018-03-03 %C Caen, France %B 35th Symposium on Theoretical Aspects of Computer Science %E Niedermeier, Rolf; Vall&#233;e, Brigitte %P 1 - 13 %Z sequence number: 5 %I Schloss Dagstuhl %@ 978-3-95977-062-0 %B Leibniz International Proceedings in Informatics %N 96 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/8518/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Journal Article %A Adamaszek, Anna %A Chalermsook, Parinya %A Ene, Alina %A Wiese, Andreas %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Submodular Unsplittable Flow on Trees : %G eng %U http://hdl.handle.net/21.11116/0000-0000-73B6-1 %R 10.1007/s10107-017-1218-4 %7 2018-01-17 %D 2018 %J Mathematical Programming / B %V 172 %N 1-2 %& 565 %P 565 - 589 %I Springer %C Berlin %@ false

%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Foerster, Klaus-Tycho %A Schmid, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Walking Through Waypoints : %G eng %U http://hdl.handle.net/21.11116/0000-0002-5765-B %R 10.1007/978-3-319-77404-6_4 %D 2018 %B 13th Latin American Theoretical Informatics Symposium %Z date of event: 2018-04-16 - 2018-04-19 %C Buenos Aires, Argentinia %B LATIN 2018: Theoretical Informatics %E Bender, Michael A.; Farach-Colton, Mart&#237;n; Mosteiro, Miguel A. %P 37 - 51 %I Springer %@ 978-3-319-77403-9 %B Lecture Notes in Computer Science %N 10807

%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Ossona de Mendez, Patrice %A Rabinovich, Roman %A Siebertz, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Distributed Domination on Graph Classes of Bounded Expansion : %G eng %U http://hdl.handle.net/21.11116/0000-0002-7081-D %R 10.1145/3210377.3210383 %D 2018 %B 30th ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2018-07-16 - 2018-07-18 %C Vienna, Austria %B SPAA'18 %P 143 - 151 %I ACM %@ 978-1-4503-5799-9

%0 Conference Proceedings %A Amiri, Saeed Akhoondian %A Dudycz, Szymon %A Schmid, Stefan %A Wiederrecht, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Congestion-Free Rerouting of Flows on DAGs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-707F-2 %R 10.4230/LIPIcs.ICALP.2018.143 %U urn:nbn:de:0030-drops-91471 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 13 %Z sequence number: 143 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9147/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Journal Article %A Amiri, Saeed Akhoondian %A Foerster, Klaus-Tycho %A Jacob, Riko %A Schmid, Stefan %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Charting the Algorithmic Complexity of Waypoint Routing : %G eng %U http://hdl.handle.net/21.11116/0000-0002-7083-B %R 10.1145/3211852.3211859 %7 2018 %D 2018 %J ACM SIGCOMM Computer Communication Review %V 48 %N 1 %& 42 %P 42 - 48 %I ACM %C New York, NY %@ false

%0 Conference Proceedings %A Antoniadis, Antonios %A Schewior, Kevin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Tight Lower Bound for Online Convex Optimization with Switching Costs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F30-5 %R 10.1007/978-3-319-89441-6_13 %D 2018 %B 15th Workshop on Approximation and Online Algorithms %Z date of event: 2017-09-07 - 2017-09-08 %C Vienna, Austria %B Approximation and Online Algorithms %E Solis-Oba, Roberto; Fleischer, Rudolf %P 164 - 165 %I Springer %@ 978-3-319-89440-9 %B Lecture Notes in Computer Science %N 10787

%0 Report %A Antoniadis, Antonios %A Fleszar, Krzysztof %A Hoeksma, Ruben %A Schewior, Kevin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T A PTAS for Euclidean TSP with Hyperplane Neighborhoods : %U http://hdl.handle.net/21.11116/0000-0002-9F37-E %U http://arxiv.org/abs/1804.03953 %D 2018 %X In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN is known to be APX-hard, which gives rise to studying more tractable special cases of the problem. In this paper, we focus on the fundamental special case of regions that are hyperplanes in the $d$-dimensional Euclidean space. This case contrasts the much-better understood case of so-called fat regions. While for $d=2$ an exact algorithm with running time $O(n^5)$ is known, settling the exact approximability of the problem for $d=3$ has been repeatedly posed as an open question. To date, only an approximation algorithm with guarantee exponential in $d$ is known, and NP-hardness remains open. For arbitrary fixed $d$, we develop a Polynomial Time Approximation Scheme (PTAS) that works for both the tour and path version of the problem. Our algorithm is based on approximating the convex hull of the optimal tour by a convex polytope of bounded complexity. Such polytopes are represented as solutions of a sophisticated LP formulation, which we combine with the enumeration of crucial properties of the tour. As the approximation guarantee approaches $1$, our scheme adjusts the complexity of the considered polytopes accordingly. In the analysis of our approximation scheme, we show that our search space includes a sufficiently good approximation of the optimum. To do so, we develop a novel and general sparsification technique to transform an arbitrary convex polytope into one with a constant number of vertices and, in turn, into one of bounded complexity in the above sense. Hereby, we maintain important properties of the polytope. %K Computer Science, Data Structures and Algorithms, cs.DS

%0 Conference Proceedings %A Antoniadis, Antonios %A Cristi, Andr&#233;s %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Near Optimal Mechanism for Energy Aware Scheduling : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9F48-B %R 10.1007/978-3-319-99660-8_4 %D 2018 %B 11th International Symposium on Algorithmic Game Theory %Z date of event: 2018-09-11 - 2018-09-14 %C Beijing, China %B Algorithmic Game Theory %E Deng, Xiaotie %P 31 - 42 %I Springer %@ 978-3-319-99659-2 %B Lecture Notes in Computer Science %N 11059

%0 Conference Proceedings %A Antoniadis, Antonios %A Fischer, Carsten %A Tonnis, Andreas %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Collection of Lower Bounds for Online Matching on the Line : %G eng %U http://hdl.handle.net/21.11116/0000-0002-5763-D %R 10.1007/978-3-319-77404-6_5 %D 2018 %B 13th Latin American Theoretical Informatics Symposium %Z date of event: 2018-04-16 - 2018-04-19 %C Buenos Aires, Argentinia %B LATIN 2018: Theoretical Informatics %E Bender, Michael A.; Farach-Colton, Mart&#237;n; Mosteiro, Miguel A. %P 52 - 65 %I Springer %@ 978-3-319-77403-9 %B Lecture Notes in Computer Science %N 10807

%0 Report %A Arunachalam, Srinivasan %A Chakraborty, Sourav %A Kouck&#253;, Michal %A Saurabh, Nitin %A de Wolf, Ronald %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Improved Bounds on Fourier Entropy and Min-entropy : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AA5A-A %U http://arxiv.org/abs/1809.09819 %D 2018 %X Given a Boolean function $f:\{-1,1\}^n\to \{-1,1\}$, the Fourier distribution assigns probability $\widehat{f}(S)^2$ to $S\subseteq [n]$. The Fourier Entropy-Influence (FEI) conjecture of Friedgut and Kalai asks if there exist a universal constant C>0 such that $H(\hat{f}^2)\leq C Inf(f)$, where $H(\hat{f}^2)$ is the Shannon entropy of the Fourier distribution of $f$ and $Inf(f)$ is the total influence of $f$. 1) We consider the weaker Fourier Min-entropy-Influence (FMEI) conjecture. This asks if $H_{\infty}(\hat{f}^2)\leq C Inf(f)$, where $H_{\infty}(\hat{f}^2)$ is the min-entropy of the Fourier distribution. We show $H_{\infty}(\hat{f}^2)\leq 2C_{\min}^\oplus(f)$, where $C_{\min}^\oplus(f)$ is the minimum parity certificate complexity of $f$. We also show that for every $\epsilon\geq 0$, we have $H_{\infty}(\hat{f}^2)\leq 2\log (\|\hat{f}\|_{1,\epsilon}/(1-\epsilon))$, where $\|\hat{f}\|_{1,\epsilon}$ is the approximate spectral norm of $f$. As a corollary, we verify the FMEI conjecture for the class of read-$k$ $DNF$s (for constant $k$). 2) We show that $H(\hat{f}^2)\leq 2 aUC^\oplus(f)$, where $aUC^\oplus(f)$ is the average unambiguous parity certificate complexity of $f$. This improves upon Chakraborty et al. An important consequence of the FEI conjecture is the long-standing Mansour's conjecture. We show that a weaker version of FEI already implies Mansour's conjecture: is $H(\hat{f}^2)\leq C \min\{C^0(f),C^1(f)\}$?, where $C^0(f), C^1(f)$ are the 0- and 1-certificate complexities of $f$, respectively. 3) We study what FEI implies about the structure of polynomials that 1/3-approximate a Boolean function. We pose a conjecture (which is implied by FEI): no "flat" degree-$d$ polynomial of sparsity $2^{\omega(d)}$ can 1/3-approximate a Boolean function. We prove this conjecture unconditionally for a particular class of polynomials. %K Computer Science, Computational Complexity, cs.CC

%0 Report %A Baldus, Julian %A Bringmann, Karl %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Fast Implementation of Near Neighbors Queries for Fr&#233;chet Distance (GIS Cup) : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E1A-E %U http://arxiv.org/abs/1803.00806 %D 2018 %X This paper describes an implementation of fast near-neighbours queries (also known as range searching) with respect to the Fr\'echet distance. The algorithm is designed to be efficient on practical data such as GPS trajectories. Our approach is to use a quadtree data structure to enumerate all curves in the database that have similar start and endpoints as the query curve. On these curves we run positive and negative filters to narrow the set of potential results. Only for those trajectories where these heuristics fail, we compute the Fr\'echet distance exactly, by running a novel recursive variant of the classic free-space diagram algorithm. Our implementation won the ACM SIGSPATIAL GIS Cup 2017. %K Computer Science, Computational Geometry, cs.CG

%0 Report %A Ballard, Grey %A Ikenmeyer, Christian %A Landsberg, J. M. %A Ryder, Nick %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T The Geometry of Rank Decompositions of Matrix Multiplication II: 3 x 3 Matrices : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3F64-9 %U http://arxiv.org/abs/1801.00843 %D 2018 %X This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and admits an unexpected symmetry group of order 12. We establish basic information regarding symmetry groups of decompositions and outline two approaches for finding new rank decompositions of $M_{\langle n\rangle}$ for larger $n$. %K Computer Science, Computational Complexity, cs.CC,

%0 Report %A Ban, Frank %A Bhattiprolu, Vijay %A Bringmann, Karl %A Kolev, Pavel %A Lee, Euiwoong %A Woodruff, David P. %+ 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 %T A PTAS for l p-Low Rank Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9D17-4 %U http://arxiv.org/abs/1807.06101 %D 2018 %X A number of recent works have studied algorithms for entrywise $\ell_p$-low rank approximation, namely, algorithms which given an $n \times d$ matrix $A$ (with $n \geq d$), output a rank-$k$ matrix $B$ minimizing $\|A-B\|_p^p=\sum_{i,j}|A_{i,j}-B_{i,j}|^p$ when $p > 0$; and $\|A-B\|_0=\sum_{i,j}[A_{i,j}\neq B_{i,j}]$ for $p=0$. On the algorithmic side, for $p \in (0,2)$, we give the first $(1+\epsilon)$-approximation algorithm running in time $n^{\text{poly}(k/\epsilon)}$. Further, for $p = 0$, we give the first almost-linear time approximation scheme for what we call the Generalized Binary $\ell_0$-Rank-$k$ problem. Our algorithm computes $(1+\epsilon)$-approximation in time $(1/\epsilon)^{2^{O(k)}/\epsilon^{2}} \cdot nd^{1+o(1)}$. On the hardness of approximation side, for $p \in (1,2)$, assuming the Small Set Expansion Hypothesis and the Exponential Time Hypothesis (ETH), we show that there exists $\delta := \delta(\alpha) > 0$ such that the entrywise $\ell_p$-Rank-$k$ problem has no $\alpha$-approximation algorithm running in time $2^{k^{\delta}}$. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC,Computer Science, Learning, cs.LG

%0 Conference Proceedings %A Becchetti, Luca %A Bonifaci, Vincenzo %A Natale, Emanuele %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Pooling or Sampling: Collective Dynamics for Electrical Flow Estimation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A953-2 %D 2018 %B 17th International Conference on Autonomous Agents and MultiAgent Systems %Z date of event: 2018-07-10 - 2018-07-15 %C Stockholm, Sweden %B AAMAS'18 %P 1576 - 1584 %I ACM %@ 978-1-4503-5649-7

%0 Report %A Becchetti, Luca %A Clementi, Andrea %A Natale, Emanuele %A Pasquale, Francesco %A Trevisan, Luca %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Finding a Bounded-Degree Expander Inside a Dense One : %G eng %U http://hdl.handle.net/21.11116/0000-0002-B967-A %U http://arxiv.org/abs/1811.10316 %D 2018 %X It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also an expander. As with other consequences of the MSS theorem, it is not clear how one would explicitly construct such a subgraph. We show that such a subgraph (although with quantitatively weaker expansion and near-regularity properties than those predicted by MSS) can be constructed with high probability in linear time, via a simple algorithm. Our algorithm allows a distributed implementation that runs in $\mathcal O(\log n)$ rounds and does $\bigO(n)$ total work with high probability. The analysis of the algorithm is complicated by the complex dependencies that arise between edges and between choices made in different rounds. We sidestep these difficulties by following the combinatorial approach of counting the number of possible random choices of the algorithm which lead to failure. We do so by a compression argument showing that such random choices can be encoded with a non-trivial compression. Our algorithm bears some similarity to the way agents construct a communication graph in a peer-to-peer network, and, in the bipartite case, to the way agents select servers in blockchain protocols. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Conference Proceedings %A Becchetti, Luca %A Clementi, Andrea %A Manurangsi, Pasin %A Natale, Emanuele %A Pasquale, Francesco %A Raghavendra, Prasad %A Trevisan, Luca %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Average Whenever You Meet: Opportunistic Protocols for Community Detection : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A957-E %R 10.4230/LIPIcs.ESA.2018.7 %U urn:nbn:de:0030-drops-94705 %D 2018 %B 26th Annual European Symposium on Algorithms %Z date of event: 2018-08-20 - 2018-08-22 %C Helsinki, Finland %B 26th Annual European Symposium on Algorithms %E Azar, Yossi; Bast, Hannah; Herman, Grzegorz %P 1 - 13 %Z sequence number: 7 %I Schloss Dagstuhl %@ 978-3-95977-081-1 %B Leibniz International Proceedings in Informatics %N 112 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9470/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Journal Article %A Becker, Ruben %A Sagraloff, Michael %A Sharma, Vikram %A Yap, Chee %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Simple Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-5717-8 %R 10.1016/j.jsc.2017.03.009 %7 2017-03-29 %D 2018 %J Journal of Symbolic Computation %V 86 %& 51 %P 51 - 96 %I Elsevier %C Amsterdam %@ false

%0 Journal Article %A Bhattacharya, Anup %A Issac, Davis %A Jaiswal, Ragesh %A Kumar, Amit %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Sampling in Space Restricted Settings : %G eng %U http://hdl.handle.net/21.11116/0000-0001-2C37-1 %R 10.1007/s00453-017-0335-z %7 2017 %D 2018 %J Algorithmica %V 80 %N 5 %& 1439 %P 1439 - 1458 %I Springer-Verlag %C New York %@ false

%0 Journal Article %A Bl&#228;ser, Markus %A Ikenmeyer, Christian %A Jindal, Gorav %A Lysikov, Vladimir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Generalized Matrix Completion and Algebraic Natural Proofs Contact Add Comment RSS-Feed : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3F5F-0 %7 2018 %D 2018 %J Electronic Colloquium on Computational Complexity (ECCC): Report Series %V 18-064 %& 1 %P 1 - 27 %I Hasso-Plattner-Institut f&#252;r Softwaretechnik GmbH %C Potsdam %@ false %U https://eccc.weizmann.ac.il/report/2018/064/

%0 Conference Proceedings %A Bl&#228;ser, Markus %A Ikenmeyer, Christian %A Jindal, Gorav %A Lysikov, Vladimir %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Generalized Matrix Completion and Algebraic Natural Proofs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-17DF-A %R 10.1145/3188745.3188832 %D 2018 %B 50th Annual ACM SIGACT Symposium on Theory of Computing %Z date of event: 2018-06-25 - 2017-06-29 %C Los Angeles, CA, USA %B STOC'18 %P 1193 - 1206 %I ACM %@ 978-1-4503-5559-9

%0 Journal Article %A Bl&#228;ser, Markus %A Jindal, Gorav %A Pandey, Anurag %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T A Deterministic PTAS for Commutative Rank of Matrix Spaces : %G eng %U http://hdl.handle.net/21.11116/0000-0002-B48E-3 %R 10.4086/toc.2018.v014a003 %7 2018 %D 2018 %J Theory of Computing %V 14 %& 1 %P 1 - 21 %Z sequence number: 3 %@ false

%0 Journal Article %A Boczkowski, Lucas %A Natale, Emanuele %A Feinerman, Ofer %A Korman, Amos %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Limits on Reliable Information Flows through Stochastic Populations : %G eng %U http://hdl.handle.net/21.11116/0000-0001-999D-2 %R 10.1371/journal.pcbi.1006195 %7 2018 %D 2018 %J PLoS Computational Biology %V 14 %N 6 %Z sequence number: e1006195 %I Public Library of Science %C San Francisco, CA %@ false

%0 Conference Proceedings %A Boczkowski, Lucas %A Feinerman, Ofer %A Korman, Amos %A Natale, Emanuele %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Limits for Rumor Spreading in Stochastic Populations : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A962-1 %R 10.4230/LIPIcs.ITCS.2018.49 %U urn:nbn:de:0030-drops-83207 %D 2018 %B 9th Innovations in Theoretical Computer Science %Z date of event: 2018-01-11 - 2018-01-14 %C Cambridge, MA, USA %B 9th Innovations in Theoretical Computer Science %E Karlin, Anna R. %P 1 - 21 %Z sequence number: 49 %I Schloss Dagstuhl %@ 978-3-95977-060-6 %B Leibniz International Proceedings in Informatics %N 94 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/8320/http://drops.dagstuhl.de/opus/volltexte/2018/8320/

%0 Journal Article %A Boissonnat, Jean-Daniel %A Dyer, Ramsay %A Ghosh, Arijit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Delaunay Triangulation of Manifolds : %G eng %U http://hdl.handle.net/11858/00-001M-0000-002C-7945-0 %R 10.1007/s10208-017-9344-1 %7 2017-02-01 %D 2018 %J Foundations of Computational Mathematics %V 18 %N 2 %& 399 %P 399 - 431 %I Springer %C New York, NY %@ false

%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Multivariate Fine-Grained Complexity of Longest Common Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E02-8 %U http://arxiv.org/abs/1803.00938 %D 2018 %X We revisit the classic combinatorial pattern matching problem of finding a longest common subsequence (LCS). For strings $x$ and $y$ of length $n$, a textbook algorithm solves LCS in time $O(n^2)$, but although much effort has been spent, no $O(n^{2-\varepsilon})$-time algorithm is known. Recent work indeed shows that such an algorithm would refute the Strong Exponential Time Hypothesis (SETH) [Abboud, Backurs, Vassilevska Williams + Bringmann, K\"unnemann FOCS'15]. Despite the quadratic-time barrier, for over 40 years an enduring scientific interest continued to produce fast algorithms for LCS and its variations. Particular attention was put into identifying and exploiting input parameters that yield strongly subquadratic time algorithms for special cases of interest, e.g., differential file comparison. This line of research was successfully pursued until 1990, at which time significant improvements came to a halt. In this paper, using the lens of fine-grained complexity, our goal is to (1) justify the lack of further improvements and (2) determine whether some special cases of LCS admit faster algorithms than currently known. To this end, we provide a systematic study of the multivariate complexity of LCS, taking into account all parameters previously discussed in the literature: the input size $n:=\max\{|x|,|y|\}$, the length of the shorter string $m:=\min\{|x|,|y|\}$, the length $L$ of an LCS of $x$ and $y$, the numbers of deletions $\delta := m-L$ and $\Delta := n-L$, the alphabet size, as well as the numbers of matching pairs $M$ and dominant pairs $d$. For any class of instances defined by fixing each parameter individually to a polynomial in terms of the input size, we prove a SETH-based lower bound matching one of three known algorithms. Specifically, we determine the optimal running time for LCS under SETH as $(n+\min\{d, \delta \Delta, \delta m\})^{1\pm o(1)}$. [...] %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS

%0 Conference Proceedings %A Bringmann, Karl %A K&#252;nnemann, Marvin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Multivariate Fine-Grained Complexity of Longest Common Subsequence : %G eng %U http://hdl.handle.net/21.11116/0000-0000-3F0E-C %R 10.1137/1.9781611975031.79 %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 1216 - 1235 %I SIAM %@ 978-1-61197-503-1

%0 Report %A Bringmann, Karl %A Husfeldt, Thore %A Magnusson, M&#229;ns %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Multivariate Analysis of Orthogonal Range Searching and Graph Distances Parameterized by Treewidth : %G eng %U http://hdl.handle.net/21.11116/0000-0002-173B-3 %U http://arxiv.org/abs/1805.07135 %D 2018 %X We show that the eccentricities, diameter, radius, and Wiener index of an undirected $n$-vertex graph with nonnegative edge lengths can be computed in time $O(n\cdot \binom{k+\lceil\log n\rceil}{k} \cdot 2^k k^2 \log n)$, where $k$ is the treewidth of the graph. For every $\epsilon>0$, this bound is $n^{1+\epsilon}\exp O(k)$, which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an algorithm of Cabello and Knauer (Comp. Geom., 2009) in the regime of non-constant treewidth can be improved by revisiting the analysis of orthogonal range searching, improving bounds of the form $\log^d n$ to $\binom{d+\lceil\log n\rceil}{d}$, as originally observed by Monier (J. Alg. 1980). We also investigate the parameterization by vertex cover number. %K Computer Science, Data Structures and Algorithms, cs.DS

%0 Report %A Bringmann, Karl %A Cabello, Sergio %A Emmerich, Michael T. M. %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Maximum Volume Subset Selection for Anchored Boxes : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E08-2 %U http://arxiv.org/abs/1803.00849 %D 2018 %X Let $B$ be a set of $n$ axis-parallel boxes in $\mathbb{R}^d$ such that each box has a corner at the origin and the other corner in the positive quadrant of $\mathbb{R}^d$, and let $k$ be a positive integer. We study the problem of selecting $k$ boxes in $B$ that maximize the volume of the union of the selected boxes. This research is motivated by applications in skyline queries for databases and in multicriteria optimization, where the problem is known as the hypervolume subset selection problem. It is known that the problem can be solved in polynomial time in the plane, while the best known running time in any dimension $d \ge 3$ is $\Omega\big(\binom{n}{k}\big)$. We show that: - The problem is NP-hard already in 3 dimensions. - In 3 dimensions, we break the bound $\Omega\big(\binom{n}{k}\big)$, by providing an $n^{O(\sqrt{k})}$ algorithm. - For any constant dimension $d$, we present an efficient polynomial-time approximation scheme. %K Computer Science, Computational Geometry, cs.CG,Computer Science, Data Structures and Algorithms, cs.DS

%0 Report %A Bringmann, Karl %A Wellnitz, Philip %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Clique-Based Lower Bounds for Parsing Tree-Adjoining Grammars : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3E2A-C %U http://arxiv.org/abs/1803.00804 %D 2018 %X Tree-adjoining grammars are a generalization of context-free grammars that are well suited to model human languages and are thus popular in computational linguistics. In the tree-adjoining grammar recognition problem, given a grammar $\Gamma$ and a string $s$ of length $n$, the task is to decide whether $s$ can be obtained from $\Gamma$. Rajasekaran and Yooseph's parser (JCSS'98) solves this problem in time $O(n^{2\omega})$, where $\omega < 2.373$ is the matrix multiplication exponent. The best algorithms avoiding fast matrix multiplication take time $O(n^6)$. The first evidence for hardness was given by Satta (J. Comp. Linguist.'94): For a more general parsing problem, any algorithm that avoids fast matrix multiplication and is significantly faster than $O(|\Gamma| n^6)$ in the case of $|\Gamma| = \Theta(n^{12})$ would imply a breakthrough for Boolean matrix multiplication. Following an approach by Abboud et al. (FOCS'15) for context-free grammar recognition, in this paper we resolve many of the disadvantages of the previous lower bound. We show that, even on constant-size grammars, any improvement on Rajasekaran and Yooseph's parser would imply a breakthrough for the $k$-Clique problem. This establishes tree-adjoining grammar parsing as a practically relevant problem with the unusual running time of $n^{2\omega}$, up to lower order factors. %K Computer Science, Computational Complexity, cs.CC,Computer Science, Data Structures and Algorithms, cs.DS

%0 Report %A Bringmann, Karl %A K&#252;nnemann, Marvin %A Nusser, Andr&#233; %+ 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 Fr&#233;chet Distance Under Translation: Conditional Hardness and an Algorithm via Offline Dynamic Grid Reachability : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E35-1 %U http://arxiv.org/abs/1810.10982 %D 2018 %X The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length $n$ in the plane, the fastest known algorithm runs in time $\tilde{\cal O}(n^{5})$ [Ben Avraham, Kaplan, Sharir '15]. This is achieved by constructing an arrangement of disks of size ${\cal O}(n^{4})$, and then traversing its faces while updating reachability in a directed grid graph of size $N := {\cal O}(n^2)$, which can be done in time $\tilde{\cal O}(\sqrt{N})$ per update [Diks, Sankowski '07]. The contribution of this paper is two-fold. First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than $\tilde{\cal O}(\sqrt{N})$, we improve this part of the algorithm: We observe that an offline variant of dynamic $s$-$t$-reachability in directed grid graphs suffices, and we solve this variant in amortized time $\tilde{\cal O}(N^{1/3})$ per update, resulting in an improved running time of $\tilde{\cal O}(n^{4.66...})$ for the discrete Fr\'echet distance under translation. Second, we provide evidence that constructing the arrangement of size ${\cal O}(n^{4})$ is necessary in the worst case, by proving a conditional lower bound of $n^{4 - o(1)}$ on the running time for the discrete Fr\'echet distance under translation, assuming the Strong Exponential Time Hypothesis. %K Computer Science, Data Structures and Algorithms, cs.DS

%0 Report %A Bringmann, Karl %A Ray Chaudhury, Bhaskar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS : %G eng %U http://hdl.handle.net/21.11116/0000-0002-57B9-C %U http://arxiv.org/abs/1810.01238 %D 2018 %X We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a sketch size and streaming space usage of $\mathcal{O}(L^{|\Sigma| - 1} \log L)$. We also prove matching unconditional lower bounds. As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an $\mathcal{O}(\textrm{min}\{nm, n + m^{{\lvert \Sigma \rvert}}\})$-time algorithm for this problem, on strings $x,y$ of length $n,m$, with $n \ge m$. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis. %K Computer Science, Data Structures and Algorithms, cs.DS,

%0 Conference Proceedings %A Bringmann, Karl %A Ray Chaudhury, Bhaskar %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9D0B-2 %R 10.4230/LIPIcs.FSTTCS.2018.40 %U urn:nbn:de:0030-drops-99390 %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: 40 %I Schloss Dagstuhl %@ 978-3-95977-093-4 %B Leibniz International Proceedings in Informatics %N 122 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9939/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Journal Article %A Bringmann, Karl %A Ikenmeyer, Christian %A Zuiddam, Jeroen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On Algebraic Branching Programs of Small Width : %G eng %U http://hdl.handle.net/21.11116/0000-0002-1B53-3 %R 10.1145/3209663 %7 2018 %D 2018 %J Journal of the ACM %V 65 %N 5 %& 1 %P 1 - 29 %Z sequence number: 32 %I ACM %C New York, NY %@ false

%0 Journal Article %A Bringmann, Karl %A Krinninger, Sebastian %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Note on Hardness of Diameter Approximation : %G eng %U http://hdl.handle.net/21.11116/0000-0001-2C44-2 %R 10.1016/j.ipl.2017.12.010 %7 2018 %D 2018 %J Information Processing Letters %V 133 %& 10 %P 10 - 15 %I Elsevier %@ false

%0 Conference Proceedings %A Bringmann, Karl %A Gawrychowski, Pawe&#322; %A Mozes, Shay %A Weimann, Oren %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (unless APSP can) : %G eng %U http://hdl.handle.net/21.11116/0000-0000-3F13-5 %R 10.1137/1.9781611975031.77 %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 1190 - 1206 %I SIAM %@ 978-1-61197-503-1

%0 Journal Article %A Bringmann, Karl %A Friedrich, Tobias %A Krohmer, Anton %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T De-anonymization of Heterogeneous Random Graphs in Quasilinear Time : %G eng %U http://hdl.handle.net/21.11116/0000-0001-F6A3-1 %R 10.1007/s00453-017-0395-0 %7 2017-11-15 %D 2018 %J Algorithmica %V 80 %N 11 %& 3397 %P 3397 - 3427 %I Springer-Verlag %C New York, NY %@ false

%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Small Hazard-free Transducers : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9FAD-9 %U http://arxiv.org/abs/1811.12369 %D 2018 %X Recently, an unconditional exponential separation between the hazard-free complexity and (standard) circuit complexity of explicit functions has been shown. This raises the question: which classes of functions permit efficient hazard-free circuits? Our main result is as follows. A \emph{transducer} is a finite state machine that transcribes, symbol by symbol, an input string of length $n$ into an output string of length $n$. We prove that any function arising from a transducer with $s$ states, that is input symbols which are encoded by $\ell$ bits, has a hazard-free circuit of size $2^{\BO(s+\ell)}\cdot n$ and depth $\BO(\ell+ s\cdot \log n)$; in particular, if $s, \ell\in \BO(1)$, size and depth are asymptotically optimal. We utilize our main result to derive efficient circuits for \emph{$k$-recoverable addition}. Informally speaking, a code is \emph{$k$-recoverable} if it does not increase uncertainty regarding the encoded value, so long as it is guaranteed that it is from $\{x,x+1,\ldots,x+k\}$ for some $x\in \NN_0$. We provide an asymptotically optimal $k$-recoverable code. We also realize a transducer with $\BO(k)$ states that adds two codewords from this $k$-recoverable code. Combined with our main result, we obtain a hazard-free adder circuit of size $2^{\BO(k)}n$ and depth $\BO(k\log n)$ with respect to this code, i.e., a $k$-recoverable adder circuit that adds two codewords of $n$ bits each. In other words, $k$-recoverable addition is fixed-parameter tractable with respect to $k$. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Computational Complexity, cs.CC

%0 Conference Proceedings %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-containing Sorting Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0001-3F69-4 %R 10.23919/DATE.2018.8342063 %D 2018 %B Design, Automation & Test in Europe Conference & Exhibition %Z date of event: 2018-03-19 - 2018-03-23 %C Dresden, Germany %B Proceedings of the 2018 Design, Automation & Test in Europe %P 521 - 526 %I IEEE %@ 978-3-9819263-1-6

%0 Report %A Bund, Johannes %A Lenzen, Christoph %A Medina, Moti %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Optimal Metastability-Containing Sorting Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-1801-2 %U http://arxiv.org/abs/1801.07549 %D 2018 %X When setup/hold times of bistable elements are violated, they may become metastable, i.e., enter a transient state that is neither digital 0 nor 1. In general, metastability cannot be avoided, a problem that manifests whenever taking discrete measurements of analog values. Metastability of the output then reflects uncertainty as to whether a measurement should be rounded up or down to the next possible measurement outcome. Surprisingly, Lenzen and Medina (ASYNC 2016) showed that metastability can be contained, i.e., measurement values can be correctly sorted without resolving metastability first. However, both their work and the state of the art by Bund et al. (DATE 2017) leave open whether such a solution can be as small and fast as standard sorting networks. We show that this is indeed possible, by providing a circuit that sorts Gray code inputs (possibly containing a metastable bit) and has asymptotically optimal depth and size. Concretely, for 10-channel sorting networks and 16-bit wide inputs, we improve by 48.46% in delay and by 71.58% in area over Bund et al. Our simulations indicate that straightforward transistor-level optimization is likely to result in performance on par with standard (non-containing) solutions. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Report %A Chalermsook, Parinya %A Schmid, Andreas %A Uniyal, Sumedha %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T A Tight Extremal Bound on the Lov&#225;sz Cactus Number in Planar Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5D0-0 %U http://arxiv.org/abs/1804.03485 %D 2018 %X A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph $G$ contains a cactus subgraph $C$ where $C$ contains at least a $\frac{1}{6}$ fraction of the triangular faces of $G$. We also show that this ratio cannot be improved by showing a tight lower bound. Together with an algorithm for linear matroid parity, our bound implies two approximation algorithms for computing "dense planar structures" inside any graph: (i) A $\frac{1}{6}$ approximation algorithm for, given any graph $G$, finding a planar subgraph with a maximum number of triangular faces; this improves upon the previous $\frac{1}{11}$-approximation; (ii) An alternate (and arguably more illustrative) proof of the $\frac{4}{9}$ approximation algorithm for finding a planar subgraph with a maximum number of edges. Our bound is obtained by analyzing a natural local search strategy and heavily exploiting the exchange arguments. Therefore, this suggests the power of local search in handling problems of this kind. %K Computer Science, Discrete Mathematics, cs.DM,Computer Science, Data Structures and Algorithms, cs.DS,Mathematics, Combinatorics, math.CO

%0 Report %A Chalermsook, Parinya %A Das, Syamantak %A Even, Guy %A Laekhanukit, Bundit %A Vaz, Daniel %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Survivable Network Design for Group Connectivity in Low-Treewidth Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A84E-A %U http://arxiv.org/abs/1802.10403 %D 2018 %X In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph $H$ that connects the root to every group. We consider a fault-tolerant variant of GST, which we call Restricted (Rooted) Group SNDP. In this setting, each group $S_i$ has a demand $k_i\in[k],k\in\mathbb N$, and we wish to find a min-cost $H\subseteq G$ such that, for each group $S_i$, there is a vertex in $S_i$ connected to the root via $k_i$ (vertex or edge) disjoint paths. While GST admits $O(\log^2 n\log h)$ approximation, its high connectivity variants are Label-Cover hard, and for the vertex-weighted version, the hardness holds even when $k=2$. Previously, positive results were known only for the edge-weighted version when $k=2$ [Gupta et al., SODA 2010; Khandekar et al., Theor. Comput. Sci., 2012] and for a relaxed variant where the disjoint paths may end at different vertices in a group [Chalermsook et al., SODA 2015]. Our main result is an $O(\log n\log h)$ approximation for Restricted Group SNDP that runs in time $n^{f(k, w)}$, where $w$ is the treewidth of $G$. This nearly matches the lower bound when $k$ and $w$ are constant. The key to achieving this result is a non-trivial extension of the framework in [Chalermsook et al., SODA 2017], which embeds all feasible solutions to the problem into a dynamic program (DP) table. However, finding the optimal solution in the DP table remains intractable. We formulate a linear program relaxation for the DP and obtain an approximate solution via randomized rounding. This framework also allows us to systematically construct DP tables for high-connectivity problems. As a result, we present new exact algorithms for several variants of survivable network design problems in low-treewidth graphs. %K Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Discrete Mathematics, cs.DM

%0 Conference Proceedings %A Chalermsook, Parinya %A Das, Syamantak %A Even, Guy %A Laekhanukit, Bundit %A Vaz, Daniel %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Survivable Network Design for Group Connectivity in Low-Treewidth Graphs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A832-8 %R 10.4230/LIPIcs.APPROX-RANDOM.2018.8 %U urn:nbn:de:0030-drops-94127 %D 2018 %B 21st International Workshop on Approximation Algorithms for Combinatorial Optimization Problems / 22nd International Workshop on Randomization and Computation %Z date of event: 2018-08-20 - 2018-08-22 %C Princeton, NJ, USA %B Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques %E Blais, Eric; Jansen, Klaus; Rolim, Jos&#233; D. P.; Steurer, David %P 1 - 19 %Z sequence number: 8 %I Schloss Dagstuhl %@ 978-3-95977-085-9 %B Leibniz International Proceedings in Informatics %N 116 %U http://drops.dagstuhl.de/opus/volltexte/2018/9412/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Chalermsook, Parinya %A Goswami, Mayank %A Kozma, L&#224;sz&#242; %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

%0 Conference Proceedings %A Chandran, L. Sunil %A Cheung, Yun Kuen %A Issac, Davis %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Spanning Tree Congestion and Computation of Generalized Gy&#246;ri-Lov&#225;sz Partition : %G eng %U http://hdl.handle.net/21.11116/0000-0002-9E67-9 %R 10.4230/LIPIcs.ICALP.2018.32 %U urn:nbn:de:0030-drops-90361 %D 2018 %B 45th International Colloquium on Automata, Languages, and Programming %Z date of event: 2018-07-09 - 2018-07-13 %C Prague, Czech Republic %B 45th International Colloquium on Automata, Languages, and Programming %E Chatzigiannakis, Ioannis; Kaklamanis, Christos; Marx, D&#225;niel; Sannella, Donald %P 1 - 14 %Z sequence number: 32 %I Schloss Dagstuhl %@ 978-3-95977-076-7 %B Leibniz International Proceedings in Informatics %N 107 %U http://drops.dagstuhl.de/opus/volltexte/2018/9036/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Chandran, L. Sunil %A Das, Anita %A Issac, Davis %A van Leeuwen, Erik Jan %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Algorithms and Bounds for Very Strong Rainbow Coloring : %G eng %U http://hdl.handle.net/21.11116/0000-0002-576A-6 %R 10.1007/978-3-319-77404-6_46 %D 2018 %B 13th Latin American Theoretical Informatics Symposium %Z date of event: 2018-04-16 - 2018-04-19 %C Buenos Aires, Argentinia %B LATIN 2018: Theoretical Informatics %E Bender, Michael A.; Farach-Colton, Mart&#237;n; Mosteiro, Miguel A. %P 625 - 639 %I Springer %@ 978-3-319-77403-9 %B Lecture Notes in Computer Science %N 10807

%0 Conference Proceedings %A Chan, Timothy M. %A van Dijk, Thomas C. %A Fleszar, Krzysztof %A Spoerhase, Joachim %A Wolff, Alexander %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Stabbing Rectangles by Line Segments - How Decomposition Reduces the Shallow-Cell Complexity : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ADEA-4 %R 10.4230/LIPIcs.ISAAC.2018.61 %U urn:nbn:de:0030-drops-100094 %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 - 13 %Z sequence number: 61 %I Schloss Dagstuhl %@ 978-3-95977-094-1 %B Leibniz International Proceedings in Informatics %N 123 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/10009/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Cheung, Yun Kuen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Steiner Point Removal - Distant Terminals Don't (Really) Bother : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AA8C-1 %R 10.1137/1.9781611975031.89 %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 1353 - 1360 %I SIAM %@ 978-1-61197-503-1

%0 Report %A Cheung, Yun Kuen %A Cole, Richard %A Tao, Yixin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Parallel Stochastic Asynchronous Coordinate Descent: Tight Bounds on the Possible Parallelism : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAF2-D %U http://arxiv.org/abs/1811.05087 %D 2018 %X Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar duration, then linear speedup is possible with up to $\Theta(\sqrt n/L_{\mathsf{res}})$ processors, where $L_{\mathsf{res}}$ is a suitable Lipschitz parameter. This paper shows the bound is tight for essentially all possible values of $L_{\mathsf{res}}$. %K Mathematics, Optimization and Control, math.OC,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Conference Proceedings %A Cheung, Yun Kuen %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society %T Multiplicative Weights Updates with Constant Step-Size in Graphical Constant-Sum Games : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AB07-6 %D 2018 %B Thirty-second Conference on Neural Information Processing Systems %Z date of event: 2018-12-02 - 2018-12-08 %C Montr&#233;al, Canada %B Advances in Neural Information Processing Systems 31 %E Bengio, S.; Wallach, H.; Larochelle, H.; Grauman, K.; Cesa-Bianchi, N.; Garnett, R. %P 3532 - 3542 %I Curran Associates %U http://papers.nips.cc/paper/7612-multiplicative-weights-updates-with-constant-step-size-in-graphical-constant-sum-games.pdf

%0 Conference Proceedings %A Cheung, Yun Kuen %A Cole, Richard %A Tao, Yixin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Dynamics of Distributed Updating in Fisher Markets : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAE9-8 %R 10.1145/3219166.3219189 %D 2018 %B Nineteenth ACM Conference on Economics and Computation %Z date of event: 2018-06-18 - 2018-06-22 %C Ithaca, NY, USA %B ACM EC'18 %P 351 - 368 %I ACM %@ 978-1-4503-5829-3

%0 Conference Proceedings %A Cheung, Yun Kuen %A Cole, Richard %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Amortized Analysis of Asynchronous Price Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAEE-3 %R 10.4230/LIPIcs.ESA.2018.18 %U urn:nbn:de:0030-drops-94812 %D 2018 %B 26th Annual European Symposium on Algorithms %Z date of event: 2018-08-20 - 2018-08-22 %C Helsinki, Finland %B 26th Annual European Symposium on Algorithms %E Azar, Yossi; Bast, Hannah; Herman, Grzegorz %P 1 - 15 %Z sequence number: 18 %I Schloss Dagstuhl %@ 978-3-95977-081-1 %B Leibniz International Proceedings in Informatics %N 112 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9481/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Report %A Cheung, Yun Kuen %A Cole, Richard %A Tao, Yixin %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T (Near) Optimal Parallelism Bound for Fully Asynchronous Coordinate Descent with Linear Speedup : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AAF5-A %U http://arxiv.org/abs/1811.03254 %D 2018 %X When solving massive optimization problems in areas such as machine learning, it is a common practice to seek speedup via massive parallelism. However, especially in an asynchronous environment, there are limits on the possible parallelism. Accordingly, we seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions $F:\mathbb{R}^n \rightarrow \mathbb{R}$ of the form $$F(x) = f(x) ~+~ \sum_{k=1}^n \Psi_k(x_k),$$ where $f:\mathbb{R}^n \rightarrow \mathbb{R}$ is a smooth convex function, and each $\Psi_k:\mathbb{R} \rightarrow \mathbb{R}$ is a univariate and possibly non-smooth convex function. Our approach is to quantify the shortfall in progress compared to the standard sequential stochastic gradient descent. This leads to a truly simple yet optimal analysis of the standard stochastic ACD in a partially asynchronous environment, which already generalizes and improves on the bounds in prior work. We also give a considerably more involved analysis for general asynchronous environments in which the only constraint is that each update can overlap with at most $q$ others, where $q$ is at most the number of processors times the ratio in the lengths of the longest and shortest updates. The main technical challenge is to demonstrate linear speedup in the latter environment. This stems from the subtle interplay of asynchrony and randomization. This improves Liu and Wright's (SIOPT'15) lower bound on the maximum degree of parallelism almost quadratically, and we show that our new bound is almost optimal. %K Mathematics, Optimization and Control, math.OC,Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Report %A Cheung, Yun Kuen %A Hoefer, Martin %A Nakhe, Paresh %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Tracing Equilibrium in Dynamic Markets via Distributed Adaptation : %G eng %U http://hdl.handle.net/21.11116/0000-0002-AE08-2 %U http://arxiv.org/abs/1804.08017 %D 2018 %X Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a significant amount of interest in algorithmic game theory, mainly for the prominent case of Fisher markets. Natural and decentralized processes like tatonnement and proportional response dynamics (PRD) converge quickly towards equilibrium in large classes of Fisher markets. Almost all of the literature assumes that the market is a static environment and that the parameters of agents and goods do not change over time. In contrast, many large real-world markets are subject to frequent and dynamic changes. In this paper, we provide the first provable performance guarantees of discrete-time tatonnement and PRD in markets that are subject to perturbation over time. We analyze the prominent class of Fisher markets with CES utilities and quantify the impact of changes in supplies of goods, budgets of agents, and utility functions of agents on the convergence of tatonnement to market equilibrium. Since the equilibrium becomes a dynamic object and will rarely be reached, our analysis provides bounds expressing the distance to equilibrium that will be maintained via tatonnement and PRD updates. Our results indicate that in many cases, tatonnement and PRD follow the equilibrium rather closely and quickly recover conditions of approximate market clearing. Our approach can be generalized to analyzing a general class of Lyapunov dynamical systems with changing system parameters, which might be of independent interest. %K Computer Science, Computer Science and Game Theory, cs.GT

%0 Journal Article %A Chiantini, Luca %A Hauenstein, Jonathan D. %A Ikenmeyer, Christian %A Landsberg, Joseph M. %A Ottaviani, Giorgio %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Polynomials and the Exponent of Matrix Multiplication : %G eng %U http://hdl.handle.net/21.11116/0000-0001-88D0-A %R 10.1112/blms.12147 %7 2018 %D 2018 %J Bulletin of the London Mathematical Society %V 50 %N 3 %& 369 %P 369 - 389 %I London Mathematical Society %C London %@ false

%0 Conference Proceedings %A Choudhary, Aruni %A Kachanovich, Siargey %A Wintraecken, Mathijs %+ Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T Coxeter Triangulations Have Good Quality : %G eng %U http://hdl.handle.net/21.11116/0000-0002-E5C4-E %D 2018 %B 34th European Workshop on Computational Geometry %Z date of event: 2018-03-21 - 2018-03-23 %C Berlin, Germany %B EuroCG 18 Extended Abstracts %P 37 - 42 %U https://conference.imp.fu-berlin.de/eurocg18/download/eurocg_proc.pdf

%0 Report %A Clementi, Andrea %A Gual&#224;, Luciano %A Natale, Emanuele %A Pasquale, Francesco %A Scornavacca, Giacomo %A Trevisan, Luca %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations External Organizations %T Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise : %G eng %U http://hdl.handle.net/21.11116/0000-0002-B985-7 %U http://arxiv.org/abs/1807.05626 %D 2018 %X Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An $\Omega(\epsilon^{-2} n)$ lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where $\epsilon$ is a parameter that measures the amount of noise). In such model, we prove a new $\Theta(\epsilon^{-2} n \log n)$ bound for Broadcast and a $\Theta(\epsilon^{-2} \log n)$ bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast. %K Computer Science, Distributed, Parallel, and Cluster Computing, cs.DC

%0 Conference Proceedings %A Clementi, Andrea %A Ghaffari, Mohsen %A Gual&#224;, Luciano %A Natale, Emanuele %A Pasquale, Francesco %A Scornavacca, Giacomo %+ External Organizations External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations External Organizations %T A Tight Analysis of the Parallel Undecided-State Dynamics with Two Colors : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A96C-7 %R 10.4230/LIPIcs.MFCS.2018.28 %U urn:nbn:de:0030-drops-96107 %D 2018 %B 43rd International Symposium on Mathematical Foundations of Computer Science %Z date of event: 2018-08-27 - 2018-08-31 %C Liverpool, UK %B 43rd International Symposium on Mathematical Foundations of Computer Science %E Potapov, Igor; Spirakis, Paul; Worrell, James %P 1 - 15 %Z sequence number: 28 %I Schloss Dagstuhl %@ 978-3-95977-086-6 %B Leibniz International Proceedings in Informatics %N 117 %@ false %U http://drops.dagstuhl.de/opus/volltexte/2018/9610/http://drops.dagstuhl.de/doku/urheberrecht1.html

%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

%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

%0 Journal Article %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A48F-4 %7 2018 %D 2018 %J Bulletin of the EATCS %O EATCS %V 125 %Z sequence number: 542 %@ false

%0 Report %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A446-6 %U http://arxiv.org/abs/1804.07223 %D 2018 %X Consider the following process on a network: Each agent initially holds either opinion blue or red; then, in each round, each agent looks at two random neighbors and, if the two have the same opinion, the agent adopts it. This process is known as the 2-Choices dynamics and is arguably the most basic non-trivial opinion dynamics modeling voting behavior on social networks. Despite its apparent simplicity, 2-Choices has been analytically characterized only on networks with a strong expansion property -- under assumptions on the initial configuration that establish it as a fast majority consensus protocol. In this work, we aim at contributing to the understanding of the 2-Choices dynamics by considering its behavior on a class of networks with core-periphery structure, a well-known topological assumption in social networks. In a nutshell, assume that a densely-connected subset of agents, the core, holds a different opinion from the rest of the network, the periphery. Then, depending on the strength of the cut between the core and the periphery, a phase-transition phenomenon occurs: Either the core's opinion rapidly spreads among the rest of the network, or a metastability phase takes place, in which both opinions coexist in the network for superpolynomial time. The interest of our result is twofold. On the one hand, by looking at the 2-Choices dynamics as a simplistic model of competition among opinions in social networks, our theorem sheds light on the influence of the core on the rest of the network, as a function of the core's connectivity towards the latter. On the other hand, to the best of our knowledge, we provide the first analytical result which shows a heterogeneous behavior of a simple dynamics as a function of structural parameters of the network. Finally, we validate our theoretical predictions with extensive experiments on real networks. %K cs.SI, Physics, Physics and Society, physics.soc-ph

%0 Conference Proceedings %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Phase Transition of the 2-Choices Dynamics on Core-Periphery Networks : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A47E-8 %D 2018 %B 17th International Conference on Autonomous Agents and MultiAgent Systems %Z date of event: 2018-07-10 - 2018-07-15 %C Stockholm, Sweden %B AAMAS'18 %P 777 - 785 %I ACM %@ 978-1-4503-5649-7

%0 Journal Article %A Cruciani, Emilio %A Natale, Emanuele %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Metastability of Quadratic Majority Dynamics on Clustered Graphs and its Biological Implications : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A94B-C %7 2018 %D 2018 %J Bulletin of the EATCS %O EATCS %V 125 %Z sequence number: 535 %@ false

%0 Conference Proceedings %A Cruciani, Emilio %A Natale, Emanuele %A Nusser, Andr&#233; %A Scornavacca, Giacomo %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T On the Emergent Behavior of the 2-Choices Dynamics : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A44E-E %D 2018 %B 19th Italian Conference on Theoretical Computer Science %Z date of event: 2018-09-18 - 2018-09-20 %C Urbino, Italy %B Proceedings of the 19th Italian Conference on Theoretical Computer Science %E Aldini, Alessandro; Bernardo, Marco %I CEUR-WS %B CEUR Workshop Proceedings %N 2243 %U http://ceur-ws.org/Vol-2243/paper4.pdf

%0 Journal Article %A Cygan, Marek %A Kratsch, Stefan %A Nederlof, Jesper %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Fast Hamiltonicity Checking Via Bases of Perfect Matchings : %G eng %U http://hdl.handle.net/21.11116/0000-0001-7AE5-4 %R 10.1145/3148227 %7 2018 %D 2018 %J Journal of the ACM %V 65 %N 3 %Z sequence number: 12 %I Association for Computing Machinery, Inc. %C New York, NY %@ false

%0 Report %A Cygan, Marek %A Kortsarz, Guy %A Laekhanukit, Bundit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On Subexponential Running Times for Approximating Directed Steiner Tree and Related Problems : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A85B-B %U http://arxiv.org/abs/1811.00710 %D 2018 %X This paper concerns proving almost tight (super-polynomial) running times, for achieving desired approximation ratios for various problems. To illustrate, the question we study, let us consider the Set-Cover problem with n elements and m sets. Now we specify our goal to approximate Set-Cover to a factor of (1-d)ln n, for a given parameter 0<d<1. What is the best possible running time for achieving such approximation? This question was answered implicitly in the work of Moshkovitz [Theory of Computing, 2015]: Assuming both the Projection Games Conjecture (PGC) and the Exponential-Time Hypothesis (ETH), any ((1-d) ln n)-approximation algorithm for Set-Cover must run in time >= 2^{n^{c d}}, for some constant 0<d<1. We study the questions along this line. First, we show that under ETH and PGC any ((1-d) \ln n)-approximation for Set-Cover requires 2^{n^{d}}-time. This (almost) matches the running time of 2^{O(n^d)} for approximating Set-Cover to a factor (1-d) ln n by Cygan et al. [IPL, 2009]. Our result is tight up to the constant multiplying the n^{d} terms in the exponent. This lower bound applies to all of its generalizations, e.g., Group Steiner Tree (GST), Directed Steiner (DST), Covering Steiner Tree (CST), Connected Polymatroid (CP). We also show that in almost exponential time, these problems reduce to Set-Cover: We show (1-d)ln n approximation algorithms for all these problems that run in time 2^{n^{d \log n } poly(m). We also study log^{2-d}n approximation for GST. Chekuri-Pal [FOCS, 2005] showed that GST admits (log^{2-d}n)-approximation in time exp(2^{log^{d+o(1)}n}), for any 0 < d < 1. We show the lower bound of GST: any (log^{2-d}n)-approximation for GST must run in time >= exp((1+o(1)){log^{d-c}n}), for any c>0, unless the ETH is false. Our result follows by analyzing the work of Halperin and Krauthgamer [STOC, 2003]. The same lower and upper bounds hold for CST. %K Computer Science, Data Structures and Algorithms, cs.DS

%0 Conference Proceedings %A David, Roee %A Karthik, C. S. %A Laekhanukit, Bundit %+ External Organizations External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society %T On the Complexity of Closest Pair via Polar-Pair of Point-Sets : %G eng %U http://hdl.handle.net/21.11116/0000-0002-A827-5 %R 10.4230/LIPIcs.SoCG.2018.28 %U urn:nbn:de:0030-drops-87412 %D 2018 %B 34th International Symposium on Computational Geometry %Z date of event: 2018-06-11 - 2018-06-14 %C Budapest, Hungary %B 34th International Symposium on Computational Geometry %E Speckmann, Bettina; T&#243;th, Csaba D. %P 1 - 15 %Z sequence number: 28 %I Schloss Dagstuhl %@ 978-3-95977-066-8 %B Leibniz International Proceedings in Informatics %N 99 %U http://drops.dagstuhl.de/opus/volltexte/2018/8741/http://drops.dagstuhl.de/doku/urheberrecht1.html

%0 Conference Proceedings %A Eden, Talya %A Levi, Reut %A Ron, Dana %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Testing Bounded Arboricity : %G eng %U http://hdl.handle.net/21.11116/0000-0004-B7C0-4 %R 10.1137/1.9781611975031.136 %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 2081 - 2092 %I SIAM %@ 978-1-61197-503-1

%0 Conference Proceedings %A Even, Guy %A Medina, Moti %A Rawitz, Dror %+ External Organizations Algorithms and Complexity, MPI for Informatics, Max Planck Society External Organizations %T Online Generalized Caching with Varying Weights and Costs : %G eng %U http://hdl.handle.net/21.11116/0000-0002-ABEA-6 %R 10.1145/3210377.3210404 %D 2018 %B 30th ACM Symposium on Parallelism in Algorithms and Architectures %Z date of event: 2018-07-16 - 2018-07-18 %C Vienna, Austria %B SPAA'18 %P 205 - 2012 %I ACM %@ 978-1-4503-5799-9