Multivariate Algorithmics

Advanced Course, 3+1

Basic Information

Lecturers:Karl Bringmann and Holger Dell
Lectures:Tuesday + Thursday, 16:15 - 18:00, Room 024 E1 4
Tutorials:Every other Thursday
First Session:October 16th, 2018
Assistants:Cornelius Brand and Marc Roth
Credits:6 CP (≃ 4 hours/week in class + 4 hours/week for exercise sheets)

We assume basic knowledge in algorithms and theoretical computer science. Therefore, required prerequisites are a basic lecture in algorithms (such as "Grundzüge von Algorithmen und Datenstrukturen") and a basic lecture in in theoretical computer science (such as "Theoretische Informatik"). The core lecture "Algorithms and Data Structures" would be helpful, but is not a formal requirement.

Exam:The exam (either oral or written) will likely be in Mid-February


This course is about fast algorithms for NP-hard problems. The approach is to measure the running time of an algorithm as a function of not just the input length, but multiple parameters of the input. For example, while a database may contain a very large amount of data, the size of the database queries is typically extremely small in comparison.

You will learn many different intriguing algorithmic techniques to deal with NP-hard problems when a secondary input parameter is small. You will be brought to the cutting edge of current research in the area of multivariate algorithmics. You will also learn about complexity results which for some computational problems show that algorithms with a faster running time may be impossible even when the chosen secondary parameter is relatively small.


The course will be based on the book "Parameterized Algorithms" by Cygan et al. (see this for a pdf). The references in the schedule below refer to chapters in this book.


Other books on the topic include:

"Parameterized Complexity Theory" by Flum and Grohe

"Fundamentals of Parameterized Complexity" by Downey and Fellows



Oct 16 HolgerIntro & Kernelization1, 2.2.1
Oct 18 HolgerKernelization2.5, 2.6
Oct 23  Bounded Search Trees3
 Oct 25   
Oct 30  Iterative Compression4
Nov 01 Holiday
Nov 06  Color Coding5.2
 Nov 08   
Nov 13  Derandomization5.6
Nov 15  Miscellaneous6
Nov 20  Pathwidth7
 Nov 22   
Nov 27  Treewidth, Courcelle's Theorem7
Nov 29  Bidimensionality7
Dec 04  Cuts and Separators8
 Dec 06   
Dec 11 KarlCuts and Separators8
Dec 13 (Karl)Algebraic Methods10
Dec 18  Algebraic Methods10
 Dec 20   
—Winter break
Jan 08  Cut & Count11.2
 Jan 10   
Jan 15  Representative Sets12.3
Jan 17  W-Hierarchy 
Jan 22 (Karl)ETH lower bounds 
 Jan 24   
Jan 29  Hardness of Kernelization 
Jan 31  SETH lower bounds 
Feb 05 Holger4-apx for treewidth 
 Feb 07