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Complexity of the Cop and Robber Guarding Game

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Book cover Combinatorial Algorithms (IWOCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7056))

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Abstract

The guarding game is a game in which several cops has to guard a region in a (directed or undirected) graph against a robber. The robber and the cops are placed on vertices of the graph; they take turns in moving to adjacent vertices (or staying), cops inside the guarded region, the robber on the remaining vertices (the robber-region). The goal of the robber is to enter the guarded region at a vertex with no cop on it. The problem is to determine whether for a given graph and given number of cops the cops are able to prevent the robber from entering the guarded region. The problem is highly nontrivial even for very simple graphs. It is known that when the robber-region is a tree, the problem is NP-complete, and if the robber-region is a directed acyclic graph, the problem becomes PSPACE-complete [Fomin, Golovach, Hall, Mihalák, Vicari, Widmayer: How to Guard a Graph? Algorithmica, DOI: 10.1007/s00453-009-9382-4]. We solve the question asked by Fomin et al. in the previously mentioned paper and we show that if the graph is arbitrary (directed or undirected), the problem becomes E-complete.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Institute for Theoretical Computer Science (ITI), Charles University, Malostranské nám, 2/25, 118 00, Prague, Czech Republic

    Robert Šámal, Rudolf Stolař & Tomas Valla

Authors
  1. Robert Šámal
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  2. Rudolf Stolař
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  3. Tomas Valla
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Editors and Affiliations

  1. Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, Australia

    Costas S. Iliopoulos

  2. Department of Computing and Software Information Technology Building, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    William F. Smyth

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Šámal, R., Stolař, R., Valla, T. (2011). Complexity of the Cop and Robber Guarding Game. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_29

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  • DOI: https://doi.org/10.1007/978-3-642-25011-8_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25010-1

  • Online ISBN: 978-3-642-25011-8

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