Abstract

We study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffice for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G.

MSC codes

  1. 49N75
  2. 91A43

Keywords

  1. pursuit-evasion games
  2. local information
  3. path planning
  4. visibility

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Published In

cover image SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics
Pages: 26 - 41
ISSN (online): 1095-7146

History

Published online: 1 August 2006

MSC codes

  1. 49N75
  2. 91A43

Keywords

  1. pursuit-evasion games
  2. local information
  3. path planning
  4. visibility

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