The Firefighter Problem: a survey of results, directions and questions

The Firefighter Problem was introduced by Bert Hartnell in 1995 at the 25th Manitoba Conference on Combinatorial Mathematics and Computing [23]. Imagine that, at time 0, a fire breaks out at a vertex of a graph G. At each subsequent time, the firefighter “defends” a vertex of G and then the fire spreads from each “burning” vertex to all of its undefended neighbours. Once a vertex is burning or defended, it remains so from then onwards. The process terminates when the fire can no longer spread. An example is given in Figure 1. In the general form of the problem, more than one fire can break out, and the fire or fires are defended by one or more firefighters. There are a number of different objectives that can be pursued, including: