Vertex-to-vertex pursuit in a graph

Nowakowski, Richard J.; Winkler, Peter

doi:10.1016/0012-365x(83)90160-7

Cited by 502 publications

(392 citation statements)

References 2 publications

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“…The cops win the game if they can move onto the robbers vertex. This game was introduced by Nowakowski and Winkler (1983), and by Aigner and Fromme (1984).…”

Section: The Cops and Robbers Gamementioning

confidence: 99%

Search and pursuit-evasion in mobile robotics

2011

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This paper surveys recent results in pursuitevasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work.

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“…The cops win the game if they can move onto the robbers vertex. This game was introduced by Nowakowski and Winkler (1983), and by Aigner and Fromme (1984).…”

Section: The Cops and Robbers Gamementioning

confidence: 99%

Search and pursuit-evasion in mobile robotics

2011

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“…At each step, each pursuer chooses a neighboring vertex of G to move to, then the evaders do the same. They then move to the corresponding vertex in G, as defined in [4], and repeat the previous step. The team of pursuers P wins if it "captures" all evaders.…”

Section: Assumptions Terminology and Definitionsmentioning

confidence: 99%

Scalable and Practical Pursuit-Evasion

Vieira¹,

Govindan²,

Sukhatme³

2009

Proceedings of the 2nd International Conference on Robotic Communication and Coordination

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Abstract-In this paper, we consider the design and implementation of practical, yet near-optimal, pursuit-evasion games. In prior work, we developed, using the theory of zero-sum games, minimal completion-time strategies for pursuit-evasion. Unfortunately, those strategies do not scale beyond a small number of robots. In this paper, we design and implement a partition strategy where pursuers capture evaders by decomposing the game into multiple multi-pursuer single-evader games. Our algorithm terminates, has bounded capture time, is robust, and is scalable in the number of robots. In our implementation, a sensor network provides sensing-at-a-distance, as well as a communication backbone that enables tighter coordination between pursuers. Our experiments in a challenging office environment suggest that this approach is near-optimal, at least for the configurations we have evaluated. Overall, our work illustrates an innovative interplay between robotics and communication.

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“…The game n-deletion is inspired by the well-known game of Cops and Robber; see [10]. There are two players: a deleter and mover.…”

Section: The Class Of N-ordered Graphsmentioning

confidence: 99%

The n‐ordered graphs: A new graph class

Bonato

Janssen

Wang

2008

Journal of Graph Theory

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Abstract. For a positive integer n, we introduce the new graph class of n-ordered graphs, which generalize partial n-trees. Several characterizations are given for the finite n-ordered graphs, including one via a combinatorial game.We introduce new countably infinite graphs R (n) , which we name the infinite random n-ordered graphs. The graphs R (n) play a crucial role in the theory of n-ordered graphs, and are inspired by recent research on the web graph and the infinite random graph. We characterize R (n) as a limit of a random process, and via an adjacency property and a certain folding operation. We prove that the induced subgraphs of R (n) are exactly the countable n-ordered graphs. We show that all countable groups embed in the automorphism group of R (n) .

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Vertex-to-vertex pursuit in a graph

Cited by 502 publications

References 2 publications

Search and pursuit-evasion in mobile robotics

Search and pursuit-evasion in mobile robotics

Scalable and Practical Pursuit-Evasion

The n‐ordered graphs: A new graph class

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