Fire containment in grids of dimension three and higher

Abstract

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].