Mixed search number and linear‐width of interval and split graphs

Fomin, Fedor V.; Heggernes, Pinar; Mihai, Rodica

doi:10.1002/net.20373

Cited by 6 publications

(1 citation statement)

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“…See [8,44,45,57,60,66,67,151,158,160,162] for results that were directly linked with search parameters. For results on graph searching on special graph classes, see [60,76,77,80,81,116,128,129,157,170]. Minimal (with respect to minors or subgraphs) graphs with small search numbers are characterized in [114,138].…”

Section: Parameters Complexity and Algorithmsmentioning

confidence: 99%

An annotated bibliography on guaranteed graph searching

Fomin

Thilikos

2008

Theoretical Computer Science

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279

165

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Section: Parameters Complexity and Algorithmsmentioning

confidence: 99%

An annotated bibliography on guaranteed graph searching

Fomin

Thilikos

2008

Theoretical Computer Science

Self Cite

279

165

View full text Add to dashboard Cite

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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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Exclusive Graph Searching

Blin

Burman²,

Nisse

2013

Lecture Notes in Computer Science

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Abstract. This paper tackles the well known graph searching problem, where a team of searchers aims at capturing an intruder in a network, modeled as a graph. All variants of this problem assume that any node can be simultaneously occupied by several searchers. This assumption may be unrealistic, e.g., in the case of searchers modeling physical searchers, or may require each individual node to provide additional resources, e.g., in the case of searchers modeling software agents. We thus investigate exclusive graph searching, in which no two or more searchers can occupy the same node at the same time, and, as for the classical variants of graph searching, we study the minimum number of searchers required to capture the intruder. This number is called the exclusive search number of the considered graph. Exclusive graph searching appears to be considerably more complex than classical graph searching, for at least two reasons: (1) it does not satisfy the monotonicity property, and (2) it is not closed under minor. Nevertheless, we design a polynomial-time algorithm which, given any tree T , computes the exclusive search number of T . Moreover, for any integer k, we provide a characterization of the trees T with exclusive search number at most k. This characterization allows us to describe a special type of exclusive search strategies, that can be executed in a distributed environment, i.e., in a framework in which the searchers are limited to cooperate in a distributed manner.

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Mixed search number and linear‐width of interval and split graphs

Abstract: We show that the mixed search number and the linear-width of interval graphs and of split graphs can be computed in linear time and in polynomial time, respectively.

Cited by 6 publications

References 20 publications

An annotated bibliography on guaranteed graph searching

An annotated bibliography on guaranteed graph searching

Network Decontamination

Exclusive Graph Searching

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