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
Fixed-Parameter Tractable Distances to Sparse Graph Classes
Jannis Bulian,Anuj Dawar +1 more
TL;DR: In this article, it was shown that the problem of determining the distance of a given graph G to a minor-closed class of sparse graphs is fixed-parameter tractable.
Proceedings ArticleDOI
lower bounds for the parameterized complexity of minimum fill-in and other completion problems
TL;DR: Lower bounds excluding the existence of subexponential algorithms for the Optimum Linear Arrangement problem are obtained, as well as improved, yet still not tight, lower bounds for Feedback Arc Set in Tournaments.
Journal ArticleDOI
Towards optimal kernel for edge-disjoint triangle packing
TL;DR: The kernelization of the Edge-Disjoint Triangle Packing problem is studied to answer the question negatively by deriving an improved 3.5k vertex kernel for the problem.
Proceedings Article
The Complexity of Width Minimization for Existential Positive Queries
Simone Bova,Hubie Chen +1 more
TL;DR: The complexity of the expressibility problem is determined, showing that it is complete for the level p of the polynomial hierarchy, and establishing existential positive logic as a maximal syntactic fragment where expressibility is decidable.
Posted Content
On Treewidth and Stable Marriage.
TL;DR: A comprehensive, complete picture of the behavior of central optimization versions of Stable Marriage with respect to treewidth is presented.