Hartnell’s firefighter game models the containment of the spreading of an undesired property within a network. It is a one-player game played in rounds on a graph in which a fire breaks out at vertices of . In each round the fire spreads to neighboring vertices unless the player defends these. The power of the player is limited in the sense that he can defend at most additional vertices of in each round. His objective is to save as many vertices as possible from burning. Most research on this game concerned the case , which already leads to hard problems even restricted to trees.
We study the game for larger values of and . We present useful properties of optimal strategies for the game on trees, efficient approximation algorithms, and bounds on the so-called surviving rate.