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 ArticleDOI
Discovering Graph Functional Dependencies
TL;DR: It is shown that GFD discovery is feasible over large-scale graphs, by providing parallel scalable algorithms for discovering GFDs that guarantee to reduce running time when more processors are used, and experimentally verify the effectiveness and scalability of the algorithms.
Journal ArticleDOI
Preprocessing subgraph and minor problems: When does a small vertex cover help?
TL;DR: These characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like q-Coloring, Odd Cycle Transversal, Chordal Deletion, @h-Transversal or Long Path, parameterized by the size of a vertex cover, but also imply new polynometric kernels for Problems like F-Minor-Free Deletions.
Proceedings ArticleDOI
Subexponential Algorithms for Partial Cover Problems
TL;DR: It was shown that on planar graphs both problems can be solved in time $2^{\cO(k)n^{\ cO(1)}$ and on parameterized complexity classes when parameterized by $k.
Proceedings ArticleDOI
Simultaneously Satisfying Linear Equations Over F_2: MaxLin2 and Max-r-Lin2 Parameterized Above Average
Robert Crowston,Michael R. Fellows,Gregory Gutin,Mark Jones,Frances A. Rosamond,Stéphan Thomassé,Anders Yeo +6 more
TL;DR: A theorem is proved which implies that Max-r-Lin2-AA[k,r] has a kernel with at most (2k-1)r variables and implies a lower bound on the maximum of a function f that maps {-1,1}^n to the set of reals and whose Fourier expansion is of degree r.
Journal ArticleDOI
Exploring the Subexponential Complexity of Completion Problems
TL;DR: It is proved that completions into several well-studied classes of graphs without long induced cycles and paths also admit parameterized subexponential time algorithms.