Abstract
This paper is a contribution to the classical cops and robber problem on a graph, directed to two-dimensional grids and tori. We apply some new concepts for solving the problem on grids and apply these concepts to give a new algorithm for the capture on tori. Then we consider using any number k of cops, give efficient algorithms for this case yielding a capture time \(t_k\), and compute the minimum value of k needed for any given capture time. We introduce the concept of work \(w_k=k\cdot t_k\) of an algorithm and study a possible speed-up using larger teams of cops.
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Luccio, F., Pagli, L. (2019). Capture on Grids and Tori with Different Numbers of Cops. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2019. Lecture Notes in Computer Science(), vol 11657. Springer, Cham. https://doi.org/10.1007/978-3-030-25636-4_34
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DOI: https://doi.org/10.1007/978-3-030-25636-4_34
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