Computing Directed Pathwidth in $$O(1.89^{n})$$ O ( 1 . 89 n ) Time

Kitsunai, Kenta; Kobayashi, Yasuaki; Komuro, Keita; Tamaki, Hisao; Tano, Toshihiro

doi:10.1007/s00453-015-0015-9

Cited by 7 publications

References 22 publications

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Directed Path-Width of Sequence Digraphs

Gurski

Rehs

Rethmann

2018

Combinatorial Optimization and Applications

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Computing the directed path-width of a directed graph is an NP-hard problem. Even for digraphs of maximum semi-degree 3 the problem remains hard. We propose a decomposition of an input digraph G = (V, A) by a number k of sequences with entries from V , such that (u, v) ∈ A if and only if in one of the sequences there is an occurrence of u appearing before an occurrence of v. We present several graph theoretical properties of these digraphs. Among these we give forbidden subdigraphs of digraphs which can be defined by k = 1 sequence, which is a subclass of semicomplete digraphs. Given the decomposition of digraph G, we show an algorithm which computes the directed path-width of G in time O(k · (1 + N ) k ), where N denotes the maximum sequence length. This leads to an XP-algorithm w.r.t. k for the directed path-width problem. Our result improves the algorithms of Kitsunai et al. for digraphs of large directed path-width which can be decomposed by a small number of sequence. A related but different concept for undirected graphs is the notation of word-representable graphs. A graph G = (V, E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if {x, y} ∈ E., see [19] for a survey.

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Directed Path-Width of Sequence Digraphs

Gurski

Rehs

Rethmann

2018

Combinatorial Optimization and Applications

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Network Decontamination

Nisse

2019

Distributed Computing by Mobile Entities

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The Network Decontamination problem consists in coordinating a team of mobile agents in order to clean a contaminated network. The problem is actually equivalent to tracking and capturing an invisible and arbitrarily fast fugitive. This problem has natural applications in network security in computer science or in robotics for search or pursuitevasion missions. Many different objectives have been studied: the main one being the minimization of the number of mobile agents necessary to clean a contaminated network. Many environments (continuous or discrete) have also been considered. In this Chapter, we focus on networks modeled by graphs. In this context, the optimization problem that consists in minimizing the number of agents has a deep graph-theoretical interpretation. Network decontamination and, more precisely, graph searching models, provide nice algorithmic interpretations of fundamental concepts in the Graph Minors theory by Robertson and Seymour. For all these reasons, graph searching variants have been widely studied since their introduction by Breish (1967) and mathematical formalizations by and Petrov (1982). This chapter consists of an overview of algorithmic results on graph decontamination and graph searching.

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Digraphs of Bounded Width

Kreutzer

Kwon

2018

Springer Monographs in Mathematics

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Computing Directed Pathwidth in $$O(1.89^{n})$$ O ( 1 . 89 n ) Time

Cited by 7 publications

References 22 publications

Directed Path-Width of Sequence Digraphs

Directed Path-Width of Sequence Digraphs

Network Decontamination

Digraphs of Bounded Width

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