Firefighting on Grids ⋆

The Firefighter Problem (FP) is a graph problem originally introduced in 1995 to model the spread of a fire in a graph, which has attracted considerable attention in the literature. The goal is to devise a strategy to employ a given sequence of firefighters on strategic points in the graph in order to contain efficiently the fire (which spreads from each unprotected vertex to all of it neighbours on successive time steps). Recently, an online version of FP— where the number of firefighters available at each turn are revealed in real-time— has been introduced in [3,4] and studied on trees. In this paper, we extend the work in [3,4] by considering the online containment of fire on square grids. In particular, we provide a set of sufficient conditions that allow to solve the online version of the firefighting problem on infinite square grids, illustrating the corresponding fire containment strategies.