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:
2010

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Abstract

We prove that the robber can evade (that is, stay at least unit distance from) at least @?n/5.889@? cops patroling an nxn 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....