Improved bounds for cops-and-robber pursuit

Laurent Alonso (1) , Edward M. Reingold (2)

1 ALICE - Geometry and Lighting
2 IIT CS - Department of Computer Science [IIT]

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.

Domaines: Algorithme et structure de données [cs.DS]; Géométrie algorithmique [cs.CG]

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