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On Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids
Preprint
2009-09-07
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Abstract
We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an \(n\)-dimensional grid, at least \(n\) cops are necessary to ensure capture of the robber. We also present a set of cop strategies for which \(n\) cops are provably sufficient to catch the robber. Further, for two-dimensional grid, we provide an efficient cop strategy for which the robber is caught even by a single cop under certain conditions.