2019/07/17 by Marc Demange, Demange, Marc, David Ellison +3
Engineering · #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #Evacuation and Crowd Dynamics #FOS: Computer and information sciences #FOS: Mathematics #Fire Detection and Safety Systems #Smart Grid Security and Resilience
paper · pdf · doi:10.48550/arxiv.1907.07450
openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the literature and studied on trees. In this paper, we consider 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.