A cops and robber game in multidimensional grids

Authors:
Sayan Bhattacharya;Goutam Paul;Swagato Sanyal
Affiliations:
Department of Computer Science, Duke University, Durham, NC 27708, USA;Department of Computer Science and Engineering, Jadavpur University, Kolkata 700 032, India;Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, India
Venue:
Discrete Applied Mathematics
Year:
2010

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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 in an n-dimensional grid, at least n cops are necessary if one wants to catch the robber for all possible initial configurations. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber. Further, we revisit the game in a two-dimensional grid and provide an independent proof of the fact that the robber can be caught even by a single cop under certain conditions.