Fire containment in grids of dimension three and higher

Details Fire containment in grids of dimension three and higher Fire containment in grids of dimension three and higher

2004-09-13

arxiv.org/abs/math/0409195v1

Mathematics

Combinatorics

15 pages, 1 figure

Scientific paper

We consider a deterministic discrete-time model of fire spread introduced by
Hartnell [1995] and the problem of minimizing the number of burnt vertices when
deploying a limited number of firefighters per timestep. We consider the
process occurring on the d-dimensional square lattice for d>=3, and we prove
several results, including two conjectures of Wang and Moeller [2002].

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