Open AccessBook
Parameterized complexity theory
Jörg Flum,Martin Grohe +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.read more
Citations
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Proceedings ArticleDOI
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Holger Dell,Dieter van Melkebeek +1 more
TL;DR: It is shown that if satisfiability for n-variable d-CNF formulas has a protocol of cost O(nd-ε) then coNP is in NP/poly, which implies that the polynomial-time hierarchy collapses to its third level.
Book
Kernelization: Theory of Parameterized Preprocessing
TL;DR: Kernelization: Theory of Parameterized Preprocessing, by Fomin et al., is unique in that it is a text focusing solely on the titular topic of kernelization, and is able to more effectively showcase and teach the tools used in the field than a more traditional text on fixed parameter complexity.
Book ChapterDOI
Graph Layout Problems Parameterized by Vertex Cover
TL;DR: This paper study's basic ingredient is a classical algorithm for Integer Linear Programming when parameterized by dimension, designed by Lenstra and later improved by Kannan, showing that all the mentioned problems are fixed parameter tractable.
Journal ArticleDOI
Survey: A survey of the algorithmic aspects of modular decomposition
Michel Habib,Christophe Paul +1 more
TL;DR: Modular decomposition is a technique that applies to (but is not restricted to) graphs as discussed by the authors, and it naturally appears in the proofs of many graph theoretical theorems, and computing the modular decomposition tree is an important preprocessing step to solve a large number of combinatorial optimization problems.
Journal ArticleDOI
A kernelization algorithm for d-Hitting Set
TL;DR: A kernelization algorithm for the 3-Hitting Set problem is presented along with a general kernelization for d-H hitting Set, which guarantees a kernel whose order does not exceed (2d-1)k^d^-^1+k.