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 Article
Backdoor trees
Marko Samer,Stefan Szeider +1 more
TL;DR: In this article, the authors introduce the notion of backdoor trees as an indicator for the presence of a hidden structure in real-world SAT instances and compare the size of backdoor sets with the number of backdoor variables.
Proceedings Article
Local search: is brute-force avoidable?
Michael R. Fellows,Frances A. Rosamond,Fedor V. Fomin,Daniel Lokshtanov,Saket Saurabh,Yngve Villanger +5 more
TL;DR: It is shown that for several classes of sparse graphs, including planar graphs, graphs of bounded vertex degree and graphs excluding some fixed graph as a minor, an improved solution in the k-exchange neighborhood for many problems can be found much more efficiently.
Journal ArticleDOI
Hardness of discrepancy computation and ε-net verification in high dimension
TL;DR: It is proved that the canonical decision problems are W[1]-hard with respect to the dimension, implying that no f( d)@?n^O^(^1^)-time algorithm is possible for any function f(d) unless FPT=W[1].
Book ChapterDOI
Constraint satisfaction with bounded treewidth revisited
Marko Samer,Stefan Szeider +1 more
TL;DR: This paper determines whether or not fixed-parameter algorithms for constraint satisfaction exist, and provides an effective fixed- parameter algorithm which is based on dynamic programming on “nice” tree decompositions.
Journal ArticleDOI
Model Counting for CNF Formulas of Bounded Modular Treewidth
TL;DR: It is shown that the number of satisfying assignments can be computed in polynomial time for CNF formulas whose incidence graphs have bounded modular treewidth, and the first one to harness this technique for #SAT.