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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Partitioning biological networks into highly connected clusters with maximum edge coverage
TL;DR: It is shown that Highly Connected Deletion is NP-hard and provided with a fixed-parameter algorithm and a kernelization and a new heuristic that finds more clusters than the method by Hartuv and Shamir is presented.
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Fixed-Parameter Algorithms for Minimum-Cost Edge-Connectivity Augmentation
Dániel Marx,László A. Végh +1 more
TL;DR: The main result is that the minimum cost augmentation of edge-connectivity from k − 1 to k with at most p new edges is fixed-parameter tractable parameterized by p and admits a polynomial kernel.
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On Enumerating Monomials and Other Combinatorial Structures by Polynomial Interpolation
TL;DR: Three new randomized algorithms for restricted classes of polynomials with a polynomial or incremental delay, and the same global running time as the classical ones are presented.
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Partially Polynomial Kernels for Set Cover and Test Cover
TL;DR: This paper shows that both $(n-k)$-Set Cover and (n- k)-Test Cover do admit “partially polynomial kernels”.
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The parameterised complexity of counting even and odd induced subgraphs
Mark Jerrum,Kitty Meeks +1 more
TL;DR: It is demonstrated that both problems are #W[1]-hard when parameterised by k, in fact proving a somewhat stronger result about counting subgraphs with a property that only holds for some subset of k-vertex sub graphs which have an even (respectively odd) number of edges.