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Randomized Pursuit-Evasion in Graphs

Adler, M., Räcke, H., Sivadasan, N., Sohler, C., & Vöcking, B. (2002). Randomized Pursuit-Evasion in Graphs. In Automata, Languages and Programming: 29th International Colloquium, ICALP 2002 (pp. 901-912). Berlin, Germany: Springer.

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Genre: Conference Paper

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Creators:
Räcke, Harald, Author
Sohler, Christian, Author
Vöcking, Berthold1, Author
Widmayer, Peter, Editor
Triguero, Francisco, Editor
Morales, Rafael, Editor
Hennessy, Matthew, Editor
Eidenbenz, Stephan, Editor
Conejo, Ricardo, Editor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, escidoc:24019

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Abstract: { We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a {\em hunter} and a {\em rabbit}. Let $G$ be any connected, undirected graph with $n$ nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is assumed to be {\em restricted} to the graph $G$: in every round, the hunter can move using at most one edge. For the rabbit we investigate two models: in one model the rabbit is restricted to the same graph as the hunter, and in the other model the rabbit is {\em unrestricted}, i.e., it can jump to an arbitrary node in every round. We say that the rabbit is {\em caught}\/ as soon as hunter and rabbit are located at the same node in a round. The goal of the hunter is to catch the rabbit in as few rounds as possible, whereas the rabbit aims to maximize the number of rounds until it is caught. Given a randomized hunter strategy for $G$, the {\em escape length} for that strategy is the worst case expected number of rounds it takes the hunter to catch the rabbit, where the worst case is with regards to all (possibly randomized) rabbit strategies. Our main result is a hunter strategy for general graphs with an escape length of only $\O(n \log (\diam(G)))$ against restricted as well as unrestricted rabbits. This bound is close to optimal since $\Omega(n)$ is a trivial lower bound on the escape length in both models. Furthermore, we prove that our upper bound is optimal up to constant factors against unrestricted rabbits. }

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Language(s): eng - English
Dates: 2003-08-262002
Publication Status: Published in print
Pages: -
Publishing info: -
Rev. Method: -
Identifiers: eDoc: 202057
Other: Local-ID: C1256428004B93B8-07C33A9C6FA1B038C1256D13002D8771-NSBV+02
Degree: -

Event

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Title: ICALP 2002
Place of Event: Málaga, Spain
Start-/End Date: 2002-07-08 - 2002-07-13

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Source 1

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Title: Automata, Languages and Programming : 29th International Colloquium, ICALP 2002
Source Genre: Proceedings
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Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 901 - 912 Identifier: ISBN: 3-540-43864-5

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Pages: - Volume / Issue: 2380 Sequence Number: - Start / End Page: - Identifier: -