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Improved bounds for cops-and-robber pursuit

Laurent Alonso 1 Edward Reingold 2
1 ALICE - Geometry and Lighting
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than sqrt(5)n and hence that [n/sqrt(5)]+1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869...n^2+O(n) cops can capture a robber in an nxnxn cube and that a robber can forever evade fewer than 0.02168...n^2+O(n) cops in that cube.
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Submitted on : Thursday, November 22, 2012 - 1:34:18 PM
Last modification on : Wednesday, July 28, 2021 - 4:58:02 PM

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Laurent Alonso, Edward Reingold. Improved bounds for cops-and-robber pursuit. Computational Geometry, Elsevier, 2011, 44 (8), pp.365-369. ⟨10.1016/j.comgeo.2011.03.001⟩. ⟨hal-00756031⟩



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