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
On the Parameterized Complexity of Reconfiguration Problems
TL;DR: This study is motivated by results establishing that for many NP-hard problems, the classical complexity of reconfiguration is PSPACE-complete, and addresses the question for several important graph properties under two natural parameterizations.
Book ChapterDOI
The undirected feedback vertex set problem has a poly( k ) kernel
Kevin Burrage,Vladimir Estivill-Castro,Michael R. Fellows,Michael A. Langston,Shev Mac,Frances A. Rosamond +5 more
TL;DR: In this article, it was shown that polynomial-time preprocessing is sufficient to reduce an initial problem instance (G,k) to a decision-equivalent simplified instance where k ≤ k, and the number of vertices of G,k is bounded by a poly(k) function of k.
Journal Article
On Parameterized Approximability.
TL;DR: This work introduces a theory of parameterized approximability, which is intended to deal with the efficient approximation of small cost solutions for optimisation problems.
Journal ArticleDOI
Complexity of semi-stable and stage semantics in argumentation frameworks
Wolfgang Dvořák,Stefan Woltran +1 more
TL;DR: This work answers two questions about the complexity of semi-stable semantics for abstract argumentation frameworks and extends these complexity bounds to the according decision problems for stage semantics and discusses two approaches towards tractability.
Journal ArticleDOI
Graph-based data clustering with overlaps
TL;DR: A complexity dichotomy is provided (polynomial-time solvable versus NP-hard) for the underlying edge modification problems, forbidden subgraph characterizations of ''cluster graphs with overlaps'', and the parameterized complexity in terms of the number of allowed edge modifications is studied.