Improved bounds for cops-and-robber pursuit

Authors:
Laurent Alonso;Edward M. Reingold
Affiliations:
INRIA-Lorraine and LORIA, Université Henri Poincaré-Nancy I, BP 239, 54506 Vandoeuvre-lès-Nancy, France;Department of Computer Science, Illinois Institute of Technology, 10 West 31st Street, Chicago, IL 60616-2987, USA
Venue:
Computational Geometry: Theory and Applications
Year:
2011

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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 5n and hence that @?n/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.