Conference Paper

Evaluating Strategies for Running from the Cops.

Conference: IJCAI 2009, Proceedings of the 21st International Joint Conference on Artificial Intelligence, Pasadena, California, USA, July 11-17, 2009
Source: DBLP


Moving target search (MTS) or the game of cops and robbers has a broad field of application reach- ing from law enforcement to computer games. Within the recent years research has focused on computing move policies for one or multiple pur- suers (cops). The present work motivates to ex- tend this perspective to both sides, thus developing algorithms for the target (robber). We investigate the game with perfect information for both play- ers and propose two new methods, named TrailMax and Dynamic Abstract Trailmax, to compute move policies for the target. Experiments are conducted by simulating games on 20 maps of the commercial computer game Baldur's Gate and measuring sur- vival time and computational complexity. We test seven algorithms: Cover, Dynamic Abstract Mini- max, minimax, hill climbing with distance heuris- tic, a random beacon algorithm, TrailMax and DA- TrailMax. Analysis shows that our methods outper- form all the other algorithms in quality, achieving up to 98% optimality, while meeting modern com- puter game computation time constraints.

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    • "In this paper, we investigate the computational complexity of deciding whether a graph has cop number at most k; this is a natural question, as the game of Cops and Robbers has applications in the field of Artificial Intelligence (see for example [10] [12]). More precisely, we study the associated decision problem C&R: Given a graph G and positive integer k, is c(G) ≤ k? C&R clearly belongs to EXPTIME (the class of decision problems solvable in exponential time), since the number of possible game states is bounded above by n k+1 , where n = |V (G)|. "
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    ABSTRACT: C&R clearly belongs to EXPTIME (the class of decision problems solvable in exponential time), since the number of possible game states is bounded above by , where . (This observation also implies that the problem is solvable in polynomial time when k is fixed in advance, rather than being considered part of the input; see also [2], [3], [5] and [9].) Goldstein and Reingold [8] showed that the generalization of C&R in which G may be directed is EXPTIME-complete. They also proved EXPTIME-completeness when the initial positions of the cops and robber are given as part of the input. More recently, Fomin, Golovach, and Prałat [7] showed that the problem is PSPACE-complete under various restrictions on the duration of the game.
    Journal of Combinatorial Theory Series B 09/2013; 111. DOI:10.1016/j.jctb.2014.11.002 · 0.98 Impact Factor
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    • "Many papers have now been written on cop number since these three early works; see the surveys [2] [16]. Cops and Robbers has even found recent application in artificial intelligence and so-called moving target search; see [17] [19]. 1.1. "
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    ABSTRACT: Meyniel's conjecture is one of the deepest open problems on the cop num-ber of a graph. It states that for a connected graph G of order n, c(G) = O(√ n). While largely ignored for over 20 years, the conjecture is receiving increasing attention. We survey the origins of and recent developments towards the solution of the conjecture. We present some new results on so-called Meyniel extremal families containing graphs of order n satisfying c(G) ≥ d √ n, where d is a constant, and on the connections with the conjecture and the minimum order of connected k-cop-win graphs.
    08/2013; 3(2). DOI:10.4310/JOC.2012.v3.n2.a6
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    • "The necessity of algorithms for pursuit tasks occur in many real-world domains. In the Artificial Intelligence literature many heuristic algorithms for variations of the problem like Moving Target Search have been studied extensively [7] [11] [12] [16] [17]. In computer games, for instance, computer-controlled agents often pursue human-controlled players and making a good strategy for pursuers is definitely a challenge [14]. "
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