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
More filters
Posted Content
Jungles, bundles, and fixed parameter tractability
Fedor V. Fomin,Michał Pilipczuk +1 more
TL;DR: In this paper, a fixed-parameter tractable (FPT) approximation algorithm for computing the path width of a tournament and more generally of a semi-complete digraph is presented.
Book ChapterDOI
Parameterized complexity of the firefighter problem
TL;DR: It is shown that Savingk-Vertices and its dual Saving All Butk- Vertices are both W[1]-hard for parameter k even for bipartite graphs, and it is proved that a lower bound to polynomial kernelization for Saving All butk- vertices is proved.
Book ChapterDOI
Stable Assignment with Couples: Parameterized Complexity and Local Search
Dániel Marx,Ildikó Schlotter +1 more
TL;DR: This work studies the Hospitals/Residents with Couples problem, a variant of the classical Stable Marriage problem, using the framework of parameterized complexity, and investigates the matching problem containing couples.
Book ChapterDOI
Fast Algorithms for Parameterized Problems with Relaxed Disjointness Constraints
TL;DR: In this paper, generalized versions of k-path, set packing, multilinear monomial testing and Hamiltonian path are considered. But the generalization is obtained by introducing a relaxation parameter, which relaxes the constraints on feasible solutions.
Journal ArticleDOI
Combinatorial filter reduction
TL;DR: It is shown that this combinatorial filter minimization problem is not fixed-parameter tractable for any of the obvious parameters, but it is fixed- Parameter tractability for a certain combination of new parameters.