Algorithmica

, Volume 77, Issue 3, pp 942–969 | Cite as

Exclusive Graph Searching

Article

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. This problem has been mainly studied for its relationship with the pathwidth of graphs. 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 introduce and investigate exclusive graph searching, in which no two or more searchers can occupy the same node at the same time. 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. Moreover, we observe that the exclusive search number of a tree may differ exponentially from the values of classical search numbers (e.g., pathwidth). Nevertheless, we design a polynomial-time algorithm which, given any n-node tree T, computes the exclusive search number of T in time \(O(n^3)\). Moreover, for any integer k, we provide a characterization of the trees T with exclusive search number at most k. Finally, we prove that the ratio between the exclusive search number and the pathwidth of a graph is bounded by its maximum degree.

Keywords

Graph searching Pathwidth Trees Exclusivity 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.CNRSSorbonne Universités, UPMC Univ Paris 06ParisFrance
  2. 2.Université d’Evry-Val-d’EssonneEvryFrance
  3. 3.LIP6 UMR 7606ParisFrance
  4. 4.LRI, CNRS, UMR-8623Université Paris SudOrsayFrance
  5. 5.InriaSophia AntipolisFrance
  6. 6.Univ. Nice Sophia AntipolisCNRS, I3S, UMR 7271Sophia AntipolisFrance

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