How Many Lions Are Needed to Clear a Grid?

@article{Berger2009HowML,
  title={How Many Lions Are Needed to Clear a Grid?},
  author={Florian Berger and Alexander Gilbers and Ansgar Gr{\"u}ne and Rolf Klein},
  journal={Algorithms},
  year={2009},
  volume={2},
  pages={1069-1086}
}
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… CONTINUE READING

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