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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Journal ArticleDOI
A Kernelisation Approach for Multiple d-Hitting Set and Its Application in Optimal Multi-Drug Therapeutic Combinations
TL;DR: This work shows that despite being NP-complete, the (α,β,d)-Hitting Set problem is fixed-parameter tractable with a kernel of size O(αdkd) when the authors parameterize by the size k of the hitting set and the maximum number α of the minimum number of hits, and takes the maximum degree d of the target sets as a constant.
Book ChapterDOI
FPT algorithms for path-transversals and cycle-transversals problems in graphs
TL;DR: Abuilding stone for the authors' algorithms is a general O*(4p) algorithm for a class of problems aiming at breaking a set of paths in a graph, provided that the set ofpaths has a special property called homogeneity.
Book ChapterDOI
Reconfiguration over Tree Decompositions
TL;DR: In this paper, the complexity of the reconfiguration version of the vertex-subset problem is investigated for graphs of bounded treewidth. But the complexity remains PSPACE-complete.
Book ChapterDOI
Structural Parameterizations of the Mixed Chinese Postman Problem
TL;DR: In this article, the authors considered the unweighted version of the MCPP and showed that the problem is fixed-parameter tractable with respect to the treewidth of the graph.
Posted Content
Treewidth reduction for constrained separation and bipartization problems
TL;DR: This work presents a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators and proves the fixed-parameter tractability of a number of well-known separation and bipartization problems with various additional restrictions.