How Many Lions Are Needed to Clear a Grid?

We consider a pursuit-evasion problem where some lions have the task to clear a grid graph whose nodes are initially contaminated. The contamination spreads one step per time unit in each direction not blocked by a lion. A vertex is cleared from its contamination whenever a lion moves to it. Brass et al. [5] showed that n/2 lions are not enough to clear the n x n-grid. In this paper, we consider the same problem in dimension d > 2 and prove that Θ(nd-1/√d) lions are necessary and sufficient to clear the nd-grid. Furthermore, we analyze a problem variant where the lions are also allowed to jump from grid vertices to non-adjacent grid vertices.

Abstract licence: CC BY

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