Algorithms Parameterized by Vertex Cover and Modular Width, through Potential Maximal Cliques

Fomin, Fedor V.; Liedloff, Mathieu; Montealegre, Pedro; Todinca, Ioan

doi:10.1007/978-3-319-08404-6_16

Cited by 7 publications

(1 citation statement)

References 20 publications

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“…We start from two recently introduced parameters: modular-width [22] and neighborhood diversity [31]. Both parameters received much attention [1,2,5,7,12,17,18,21,24,25,29] also due to their property of being computable in polynomial time [22,31].…”

Section: Introductionmentioning

confidence: 99%

Iterated Type Partitions

Cordasco

Gargano

Rescigno

2020

Lecture Notes in Computer Science

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This paper introduces a novel parameter, called iterated type partition, that can be computed in polynomial time and nicely places between modular-width and neighborhood diversity. We prove that the Equitable Coloring problem is W[1]-hard when parametrized by the iterated type partition. This result extends to modular-width, answering an open question on the complexity of Equitable Coloring when parametrized by modular-width. On the contrary, we show that the Equitable Coloring problem is FPT when parameterized by neighborhood diversity. Furthermore, we present a scheme for devising FPT algorithms parameterized by iterated type partition, which enables us to find optimal solutions for several graph problems. While the considered problems are already known to be FPT with respect to modular-width, the novel algorithms are both simpler and more efficient. As an example, in this paper, we give an algorithm for the Dominating Set problem that outputs an optimal set in time O(2 t + poly(n)), where n and t are the size and the iterated type partition of the input graph, respectively.

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Section: Introductionmentioning

confidence: 99%

Iterated Type Partitions

Cordasco

Gargano

Rescigno

2020

Lecture Notes in Computer Science

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Parameterized Algorithms for Parity Games

Gajarský

Lampis

Makino

et al. 2015

Mathematical Foundations of Computer Science 2015

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International audienceDetermining the winner of a Parity Game is a major problem in computational complexity with a number of applications in verification. In a parameterized complexity setting, the problem has often been considered with parameters such as (directed versions of) treewidth or clique-width, by applying dynamic programming techniques.In this paper we adopt a parameterized approach which is more inspired by well-known (non-parameterized) algorithms for this problem. We consider a number of natural parameterizations, such as by Directed Feedback Vertex Set, Distance to Tournament, and Modular Width. We show that, for these parameters, it is possible to obtain recursive parameterized algorithms which are simpler, faster and only require polynomial space. We complement these results with some algorithmic lower bounds which, among others, rule out a possible avenue for improving the best-known sub-exponential time algorithm for parity games

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Maximum Minimal Vertex Cover Parameterized by Vertex Cover

Zehavi

2015

Mathematical Foundations of Computer Science 2015

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Algorithms Parameterized by Vertex Cover and Modular Width, through Potential Maximal Cliques

Cited by 7 publications

References 20 publications

Iterated Type Partitions

Iterated Type Partitions

Parameterized Algorithms for Parity Games

Maximum Minimal Vertex Cover Parameterized by Vertex Cover

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