inria-00476686
https://inria.hal.science/inria-00476686
https://inria.hal.science/inria-00476686/document
https://inria.hal.science/inria-00476686/file/cops_journal_2008_10_16.pdf
doi:10.1016/j.tcs.2009.12.010
[UNICE] Université Nice Sophia Antipolis
[CNRS] CNRS - Centre national de la recherche scientifique
[INRIA] INRIA - Institut National de Recherche en Informatique et en Automatique
[INRIA-SOPHIA] INRIA Sophia Antipolis - Méditerranée
[I3S] Laboratoire d'Informatique, Signaux et Systèmes de Sophia-Antipolis
[INRIASO] INRIA-SOPHIA
[INRIA_TEST] INRIA - Institut National de Recherche en Informatique et en Automatique
[TESTALAIN1] TESTALAIN1
[INRIA-CHILE] INRIA Chile
[INRIA2] INRIA 2
[TDS-MACS] Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes
[UNIV-COTEDAZUR] Université Côte d'Azur
Pursuing a fast robber on a graph
Fomin, Fedor V.
Golovach, Petr A.
Kratochvil, Jan
Nisse, Nicolas
Suchan, Karol
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
ART
The Cops and Robbers game is played on undirected graphs where a group of cops tries to catch a robber. The game was deﬁned independently by Winkler-Nowakowski and Quilliot in the 1980s and since that time has been studied intensively. Despite of that, its computation complexity is still an open question. In this paper we prove that computing the minimum number of cops that can catch a robber on a given graph is NP-hard. Also we show that the parameterized version of the problem is W[2]-hard. Our proof can be extended to the variant of the game where the robber can move s times faster than the cops. We also provide a number of algorithmic and complexity results on classes of chordal graphs and on graphs of bounded cliquewidth. For example, we show that when the velocity of the robber is twice the cop's velocity, the problem is NP-hard on split graphs, while it is polynomial time solvable on split graphs when players have the same speed. Also we establish that on graphs of bounded cliquewidth (this class of graphs contains, for example, graphs of bounded treewidth), the problem is solvable in polynomial time in the case the robber's speed is at most twice the speed of cops. Finally, we show that if the robber is faster than the cops then the minimum number of cops is unbounded for planar graphs.
2010
2010-04-27
en
Theoretical Computer Science
Elsevier