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
Interval scheduling and colorful independent sets
TL;DR: In this article, the authors studied the parameterized complexity of Independent Set on 2-union graphs and on subclasses like strip graphs and showed that the problem is fixed-parameter tractable with respect to the parameter $$k$$k.
Journal ArticleDOI
Quantifying hybridization in realistic time
TL;DR: A new fixed-parameter algorithm for computing the minimum number of hybridization events for when two rooted binary phylogenetic trees are given is given, based on interleaving-a technique using repeated kernelization steps that are applied throughout the exhaustive search part of a fixed- parameter algorithm.
Journal ArticleDOI
Chamberlin--Courant Rule with Approval Ballots: Approximating the MaxCover Problem with Bounded Frequencies in FPT Time
Piotr Skowron,Piotr Faliszewski +1 more
TL;DR: This work considers the problem of winner determination under Chamberlin-Courant's multiwinner voting rule with approval utilities and shows exponential-time/FPT approximation algorithms that achieve arbitrarily good approximation ratios and have running times much better than known exact algorithms.
Journal ArticleDOI
Kernel bounds for path and cycle problems
TL;DR: This work explores the existence of polynomial kernels for various path and cycle problems, by considering nonstandard parameterizations, and shows polynometric kernels when the parameters are a given vertex cover, a modulator to a cluster graph, or a (promised) max leaf number.
Book ChapterDOI
Fixed-Parameter Algorithms for Kemeny Scores
TL;DR: This work provides first, encouraging fixed-parameter tractability results for computing optimal scores, and second, extending the results to votes with ties and incomplete votes, thus, having no longer permutations as input.