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
On the computational complexity of Ham-Sandwich cuts, Helly sets, and related problems
TL;DR: The technique of embedding d-Sum into a geometric setting is conceptually much simpler than direct fpt-reductions from purely combinatorial W[1]-hard problems and has great potential to show (parameterized) hardness and (conditional) lower bounds for many other problems.
Journal ArticleDOI
Feedback Vertex Set Inspired Kernel for Chordal Vertex Deletion
TL;DR: In this article, a polynomial kernel of size O (k12 log 10k) was proposed, which is the smallest known kernel for CVD of size at most 4.
Journal ArticleDOI
Model Checking Existential Logic on Partially Ordered Sets
TL;DR: This work investigates structural properties of posets yielding conditions for fixed-parameter tractability when the problem is parameterized by the sentence, and proves that model checking existential logic on classes of finite posets of bounded width is fixed- parameter tractable.
Book ChapterDOI
Characterizing arithmetic circuit classes by constraint satisfaction problems
TL;DR: The first natural non-circuit characterization of VP, the class of polynomial families efficiently computable by arithmetic circuits, is given.
Book ChapterDOI
Deconstructing Intractability: A Case Study for Interval Constrained Coloring
TL;DR: Several positive (fixed-parameter) tractability results are presented and a large spectrum of combinatorial research challenges for Interval Constrained Coloring is identified, based on a thorough analysis of the known NP-hardness proof.