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
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Fixed-parameter tractability results for full-degree spanning tree and its dual
TL;DR: First‐time fixed‐parameter tractability results for the NP‐hard problems MAXIMUM FULL‐DEGREE SPANNING TREE (FDST) and MINIMUM‐VERTEX FEEDBACK EDGE SET are provided and a dynamic programing algorithm for graphs of bounded treewidth is presented.
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The label cut problem with respect to path length and label frequency
Peng Zhang,Bin Fu +1 more
TL;DR: This work identifies two useful parameters, l max and f max, which are two complexity thresholds for Label s - t Cut and the Global Label Cut problems, and gives an FPT algorithm and a polynomial time exact algorithm for these two problems.
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The Complexity of Weighted Counting for Acyclic Conjunctive Queries
Arnaud Durand,Stefan Mengel +1 more
TL;DR: This paper shows that weighted counting for quantifier free ACQ is still tractable and that even minimalistic extensions of the problem lead to hard cases, and introduces a new parameter for quantified queries that permits to isolate a large island of tractability.
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On the hardness of losing weight
Andrei Krokhin,Dániel Marx +1 more
TL;DR: In this paper, the complexity of local search for the Boolean constraint satisfaction problem (CSP) was studied, and it was shown that there is a considerable amount of such problems that are NP-hard, but fixed-parameter tractable when parameterized by the distance.
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A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees
TL;DR: Using simulations, CycleKiller and NonbinaryCycleKiller are presented, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations.