Connected graph searching

Barrière, Lali; Flocchini, Paola; Fomin, Fedor V.; Fraigniaud, Pierre; Nisse, Nicolas; Santoro, Nicola; Thilikos, Dimitrios M.

doi:10.1016/j.ic.2012.08.004

Cited by 35 publications

(33 citation statements)

References 41 publications

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“…One of the interesting topics regarding this model of graph searching is the price of connectivity, that is, the ratio of the connected search number and the classical search number. For results and discussions on this issue see, e.g., [3,4,7,17,37]. For surveys on connected graph searching we refer the reader to [1,25].…”

Section: Related Workmentioning

confidence: 99%

“…A typical restriction is that the strategy needs to be monotone, that is, each edge or vertex that has been cleared (i.e., is guaranteed to be free of the fugitive) must remain clear forever, see e.g. [3,38]. In such a setting, the computation of the strategy cannot be preceded by an exploration stage, and thus the strategy is formed online.…”

Section: Introductionmentioning

confidence: 99%

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Distributed graph searching with a sense of direction

2014

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In this work we consider the edge searching problem for vertex-weighted graphs with arbitrarily fast and invisible fugitive. The weight function ω provides for each vertex v the minimum number of searchers required to guard v, i.e., the fugitive may not pass through v without being detected only if at least ω(v) searchers are present at v. This problem is a generalization of the classical edge searching problem, in which one has ω ≡ 1. We assume that with a graph G to be searched, there is associated a partition (V 1 , . . . , V t ) of its vertex set such that edges are allowed only within each V i and between two consecutive V i 's. We provide an algorithm for distributed monotone connected edge searching of such graphs, where the searchers are initially placed on an arbitrary vertex of G and have no a priori knowledge on G, but they have a sense of direction that lets them recognize whether an edge incident to already explored vertex in V i leads to a vertex in one of V i−1 , V i or V i+1 . Starting from any vertex the algorithm uses at most 3·max i=1,...,t ω(V i )+1 searchers, where ω(V i ) = v∈V i ω(v). We also prove that this algorithm is best possible up to a small additive constant, that is, each distributed searching algorithm in worst case must use 3 · max i=1,...,t ω(V i ) − 1 searchers for some graphs.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed graph searching with a sense of direction

2014

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“…Other classical variants of graph searching are node-search [3], edge-search [21,22], connected-search [2], etc. All these variants suffer from two serious limitations as far as practical applications are concerned.…”

Section: Introductionmentioning

confidence: 99%

“…We restrict ourselves to the more realistic internal search strategies [2], in which searchers are limited to move along the edges of the graph, that is, restricted to satisfy the internality constraint.…”

Section: Introductionmentioning

confidence: 99%

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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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Connected search for a lazy robber

Adler

Paul

Thilikos

2021

Journal of Graph Theory

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The node-search game against a lazy (or, respectively, agile) invisible robber has been introduced as a searchgame analogue of the treewidth parameter (and, respectively, pathwidth). In the connected variants of the above games, we additionally demand that, at each moment of the search, the clean territories are connected.1 Interestingly, the motivating story of one of the foundational articles on graph searching, authored by Torrence Parsons [46] in 1976, was inspired by an earlier article of Breisch in Southwestern Cavers Journal [13] proposing a "speleotopological" approach for the problem of finding an explorer lost in a system of dark caves. It is worth to stress that that setting neglected the natural connectivity requirement.

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Connected graph searching

Cited by 35 publications

References 41 publications

Distributed graph searching with a sense of direction

Distributed graph searching with a sense of direction

Exclusive Graph Searching

Connected search for a lazy robber

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