R. Borie, C. Tovey and S. Koenig. Algorithms and Complexity Results for Pursuit-Evasion Problems. In International Joint Conference on Artificial Intelligence (IJCAI), pages 59-66, 2009.

Abstract: We study pursuit-evasion problems where a number of pursuers have to clear a given graph. We study when polynomial-time algorithms exist to determine how many pursuers are needed to clear a given graph and how a given number of pursuers should move on the graph to clear it with either a minimum sum of their travel distances or minimum task-completion time. We generalize prior work to both unit-width arbitrary-length and unit-length arbitrary-width graphs and derive both algorithms and complexity results for a variety of graph topologies. In this context, we describe a polynomial-time algorithm, called CLEARTHETREE, that is much shorter and algorithmically simpler than the state-of-the-art algorithm for the minimum pursuer problem on trees. Our theoretical research lays a firm theoretical foundation for pursuit evasion on graphs and informs practitioners about which problems are easy and which ones are hard.

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