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arXiv · 0909.1381

On Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids

Sayan Bhattacharya·Goutam Paul·Swagato Sanyal
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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.

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Sayan Bhattacharya, Goutam Paul, Swagato Sanyal. 2009-09-08. On Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids. https://doi.org/10.1016/j.dam.2010.06.014

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