Some results about pursuit games on metric spaces obtained through graph theory techniques
European Journal of Combinatorics
The complexity of pursuit on a graph
Theoretical Computer Science
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
The Guarding Problem --- Complexity and Approximation
Combinatorial Algorithms
Pursuing a fast robber on a graph
Theoretical Computer Science
Journal of Computer and System Sciences
Cop-robber guarding game with cycle robber-region
Theoretical Computer Science
Algorithmica
Guard games on graphs: keep the intruder out!
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
The guarding game is E-complete
Theoretical Computer Science
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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.