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Bounds for Cops and Robber Pursuit

Laurent Alonso 1 Edward M. Reingold 2 
1 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove that the robber can evade (that is, stay at least unit distance from) at least $\lfloor n/5.889 \rfloor$ cops patroling an $n \times n$ continuous square region, that a robber can always evade a single cop patroling a square with side length $4$ or larger, and that a single cop on patrol can always capture the robber in a square with side length smaller than $2.189\cdots$.
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Submitted on : Wednesday, February 24, 2010 - 9:26:24 AM
Last modification on : Friday, November 18, 2022 - 9:28:11 AM

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Laurent Alonso, Edward M. Reingold. Bounds for Cops and Robber Pursuit. Computational Geometry, 2010, 43 (9), pp.749-766. ⟨10.1016/j.comgeo.2010.02.002⟩. ⟨inria-00459460⟩



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