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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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Citations
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Proceedings ArticleDOI

Decomposing Quantified Conjunctive (or Disjunctive) Formulas

Hubie Chen, +1 more
TL;DR: A comprehensive classification of the sets of prefixed graphs on which model checking is tractable is given, based on a novel generalization of treewidth, that generalizes and places into a unified framework a number of existing results.
Book ChapterDOI

Fine-grained parameterized complexity analysis of graph coloring problems

Lars Jaffke, +1 more
TL;DR: In this paper, a fine-grained analysis of the complexity of q-coloring with respect to a hierarchy of parameters is presented. Androulaki et al. showed that unless the Strong Exponential-Time Hypothesis (\(\mathsf{SETH}) fails, there is no universal constant such that q-Coloring parameterized by vertex cover can be solved in time in polynomial time for all fixed q.
Book ChapterDOI

Contractions of planar graphs in polynomial time

Marcin Kamiński, +2 more
TL;DR: It is proved that for every graph H, there exists a polynomial-time algorithm deciding if a planar graph can be contracted to H, and how to reduce finding embedded topological minors in plane graphs to solving an instance of the disjoint paths problem is shown.
Proceedings ArticleDOI

Stable Marriage with Multi-Modal Preferences

Jiehua Chen, +2 more
TL;DR: In this paper, a generalized version of the Stable marriage problem based on multi-modal preference lists is studied, where each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way.
Posted Content

A structural approach to kernels for ILPs: Treewidth and Total Unimodularity

Bart M. P. Jansen, +1 more
- 25 Jun 2015 - 
TL;DR: In this paper, the authors study the effect of subsystems with bounded treewidth or totally unimodularity on the kernelizability of the ILP feasibility problem and show that, on the positive side, if these subsystems have a small number of variables on which they interact with the remaining instance, then they can efficiently replace them by smaller subsystems of size polynomial in the domain without changing feasibility.