A witness version of the Cops and Robber game

Clarke, Nancy E.

doi:10.1016/j.disc.2008.09.032

Cited by 17 publications

(12 citation statements)

References 5 publications

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“…One might try to change the rules of the game slightly in order to get a more approachable problem, and/or to understand what property of the original game causes the difficulty. Thus, various variations of the game have been studied [2,7,11,20,23]. The approach chosen by Fomin, Golovach, Kratochvíl, Nisse, and Suchan [18] is to allow the robber to move faster than the cops.…”

Section: Introductionmentioning

confidence: 99%

Chasing a Fast Robber on Planar Graphs and Random Graphs

Alon

Mehrabian

2014

J. Graph Theory

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We consider a variant of the Cops and Robber game, in which the robber has unbounded speed, i.e., can take any path from her vertex in her turn, but she is not allowed to pass through a vertex occupied by a cop. Let c ∞ (G) denote the number of cops needed to capture the robber in a graph G in this variant, and let tw(G) denote the treewidth of G. We show that if G is planar then c ∞ (G) = Θ(tw(G)), and there is a constant-factor approximation algorithm for computing c ∞ (G). We also determine, up to constant factors, the value of c ∞ (G) of the Erdős-Rényi random graph G = G(n, p) for all admissible values of p, and show that when the average degree is ω(1), c ∞ (G) is typically asymptotic to the domination number.

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Section: Introductionmentioning

confidence: 99%

Chasing a Fast Robber on Planar Graphs and Random Graphs

Alon

Mehrabian

2014

J. Graph Theory

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“…We will denote the class of cop-win graphs for this version of the game by CWFR(s, s ′ ). A witness version of the cop and robber game was recently introduced by Clarke [18]. In this game, the robber has unit speed and moves by having perfect information about cop positions.…”

Section: Introductionmentioning

confidence: 99%

Cop and Robber Games When the Robber Can Hide and Ride

Chalopin¹,

Chepoi²,

Nisse³

et al. 2011

SIAM J. Discrete Math.

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In the classical cop and robber game, two players, the cop C and the robber R, move alternatively along edges of a finite graph G = (V, E). The cop captures the robber if both players are on the same vertex at the same moment of time. A graph G is called cop win if the cop always captures the robber after a finite number of steps. Nowakowski, Winkler (1983) andQuilliot (1983) characterized the cop-win graphs as graphs admitting a dismantling scheme. In this paper, we characterize in a similar way the class CWF R(s, s ′ ) of cop-win graphs in the game in which the cop and the robber move at different speeds s ′ and s, s ′ ≤ s. We also establish some connections between cop-win graphs for this game with s ′ < s and Gromov's hyperbolicity. In the particular case s ′ = 1 and s = 2, we prove that the class of cop-win graphs is exactly the well-known class of dually chordal graphs. We show that all classes CWF R(s, 1), s ≥ 3, coincide and we provide a structural characterization of these graphs. We also investigate several dismantling schemes necessary or sufficient for the cop-win graphs in the game in which the robber is visible only every k moves for a fixed integer k > 1. We characterize the graphs which are cop-win for any value of k. Finally, we consider the game where the cop wins if he is at distance at most 1 from the robber and we characterize via a specific dismantling scheme the bipartite graphs where a single cop wins in this game.

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“…Issues about pursuit and evasion, modeled as 'PursuitEvasion Games' [1], [2], 'Homicidal Chauffeur Games' [3], 'Cop-Robber Games' [4], etc, have been widely studied in the field of mathematics [5]- [7]. In these models, one or a group of agents, called pursuers, need to detect, chase and finally capture another group of agents, called evaders.…”

Section: Introductionmentioning

confidence: 99%

Auction based task assignment for pursuit-evasion game in wireless sensor network

Chen

Yang

et al. 2012

Proceedings of the 10th World Congress on Intelligent Control and Automation

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In this paper, we address pursuit-evasion games with the auxiliary of wireless sensor network. Wireless sensor network can provide global information, such as the positions of evaders, for pursuers to improve the performance. However, some ready strategies cannot be used directly because of the positioning errors of wireless sensor network. By analyzing the performance of Lion Strategy, A Lion-Mirror-Tackle Strategy is proposed for single evader model to assign the roles of pursuers and reduce the time and energy consumptions of capture. In the multi-pursuer multi-evaders model, evaders are assigned for several groups of pursuers and a decentralized and realtime assignment strategy based on auction process is proposed, to provide fast response to the motion of evaders. The simulation shows the efficiency of our algorithms.

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A witness version of the Cops and Robber game

Cited by 17 publications

References 5 publications

Chasing a Fast Robber on Planar Graphs and Random Graphs

Chasing a Fast Robber on Planar Graphs and Random Graphs

Cop and Robber Games When the Robber Can Hide and Ride

Auction based task assignment for pursuit-evasion game in wireless sensor network

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