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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Quadratic Kernelization for Convex Recoloring of Trees
Hans L. Bodlaender,Michael R. Fellows,Michael A. Langston,Mark A. Ragan,Frances A. Rosamond,Mark Weyer +5 more
TL;DR: This paper shows that CR has a kernel of size O(k2) and describes a search-tree based FPT algorithm with a running time of O( k(k/log k)kn4) that solves the Convex Recoloring problem.
Journal ArticleDOI
Parameterized Algorithms for (r;l)-Partization
R. Krithika,N. S. Narayanaswamy +1 more
TL;DR: This work considers the problem of nding a set of at most k vertices whose deletion results in a graph that can be partitioned into r independent sets and l cliques, and describes an O (2 k ) algorithm for perfect graphs.
Journal ArticleDOI
Parameterized complexity of a coupled-task scheduling problem
TL;DR: It is proved that it is fixed-parameter tractable ($$\mathsf {FPT}$$FPT) parameterized by k the standard parameter if the total duration of each task is bounded by a constant, whereas the problem becomes hard otherwise.
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Subexponential fixed-parameter tractability of cluster editing
TL;DR: It is shown that, unless ETH fails, for any constant 0 < s <= 1, there is p = Theta(k^s) such that there is no algorithm deciding in time 2^o(sqrt(pk)) n^O(1) whether G can be transformed into a cluster graph with p cliques by changing at most k adjacencies.
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Achieving Fully Proportional Representation: Approximability Results
TL;DR: The complexity of (approximate) winner determination under the Monroe and Chamberlin-Courant multiwinner voting rules, which determine the set of representatives by optimizing the total satisfaction or dissatisfaction of the voters with their representatives, is studied.