Cops and Robber Game in Multidimensional Grids
نویسندگان
چکیده
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 under all possible initial configurations. We also present a set of cop strategies for which n cops are provably sufficient to catch the robber.
منابع مشابه
A cops and robber game in multidimensional grids
We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional 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...
متن کاملOn Necessary and Sufficient Number of Cops in the Game of Cops and Robber in Multidimensional Grids
We theoretically analyze the Cops and Robber Game for the first time in a multidimensional grid. It is shown that for an ndimensional 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...
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