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Pursuing a fast robber on a graph

Fomin, Fedor V. ; Golovach, Petr A. ; Kratochvíl, Jan ; Nisse, Nicolas ; Suchan, Karol

Theoretical computer science, 2010-02, Vol.411 (7), p.1167-1181 [Periódico revisado por pares]

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Título:
Pursuing a fast robber on a graph
Autor: Fomin, Fedor V. ; Golovach, Petr A. ; Kratochvíl, Jan ; Nisse, Nicolas ; Suchan, Karol
Assuntos: Applied sciences ; Cliquewidth ; Complexity ; Computer Science ; Computer science; control theory; systems ; Cops and Robbers ; Discrete Mathematics ; Exact sciences and technology ; Information retrieval. Graph ; Miscellaneous ; Parameterized complexity ; Planar graph ; Pursuit-evasion game on graphs ; Theoretical computing
É parte de: Theoretical computer science, 2010-02, Vol.411 (7), p.1167-1181
Descrição: The Cops and Robbers game as originally defined independently by Quilliot and by Nowakowski and Winkler in the 1980s has been much studied, but very few results pertain to the algorithmic and complexity aspects of it. In this paper we prove that computing the minimum number of cops that are guaranteed to catch a robber on a given graph is NP-hard and that the parameterized version of the problem is W[2]-hard; the proof extends to the case where the robber moves s time faster than the cops. We show that on split graphs, the problem is polynomially solvable if s = 1 but is NP-hard if s = 2 . We further prove that on graphs of bounded cliquewidth the problem is polynomially solvable for s ≤ 2 . Finally, we show that for planar graphs the minimum number of cops is unbounded if the robber is faster than the cops.
Editor: Oxford: Elsevier B.V
Idioma: Inglês

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