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Parameterized complexity theory

Jörg Flum, +1 more
TLDR
Fixed-Parameter Tractability.
Abstract: 
Fixed-Parameter Tractability.- Reductions and Parameterized Intractability.- The Class W[P].- Logic and Complexity.- Two Fundamental Hierarchies.- The First Level of the Hierarchies.- The W-Hierarchy.- The A- Hierarchy.- Kernelization and Linear Programming Techniques.- The Automata-Theoretic Approach.- Tree Width.- Planarity and Bounded Local Tree Width.- Homomorphisms and Embeddings.- Parameterized Counting Problems.- Bounded Fixed-Parameter Tractability.- Subexponential Fixed-Parameter Tractability.- Appendix, Background from Complexity Theory.- References.- Notation.- Index.

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Preventing Unraveling in Social Networks Gets Harder

Rajesh Chitnis, +2 more
- 23 Apr 2013 - 
TL;DR: Improved hardness results for the Anchored-Core problem are given, which shows that the problem is FPT on planar graphs parameterized by b for all k, even if the maximum degree of the graph is $k+2.
Proceedings ArticleDOI

A polynomial kernel for multicut in trees

Nicolas Bousquet, +3 more
TL;DR: It is shown that the Multicut In Trees problem, which consists in deciding, given a tree, a set of requests and an integer k, has a polynomial kernel.
Journal ArticleDOI

The complexity of nonrepetitive coloring

Dániel Marx, +1 more
- 01 Jan 2009 - 
TL;DR: It is shown that determining whether a particular coloring of a graph is nonrepetitive is coNP-hard, even if the number of colors is limited to four, and the problem becomes fixed-parameter tractable, if the authors only exclude colorings xx up to a fixed length k of x.
Journal ArticleDOI

A selection of useful theoretical tools for the design and analysis of optimization heuristics

Gregory Gutin, +1 more
- 01 Mar 2009 - 
TL;DR: A brief description of a selection of theoretical tools that can be used for designing and analyzing various heuristics, including several examples of preprocessing procedures and probabilistic instance analysis methods are given.
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Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey

Gregory Gutin, +1 more
- 24 Aug 2011 - 
TL;DR: This work considers constraint satisfaction problems parameterized above or below tight bounds, and discusses results, both polynomial kernels and parameterized algorithms, obtained for the problems mainly in the last few years.