AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 43 (2009), Pages 57–77 The Firefighter Problem: A survey of results, directions and questions

Imagine that a fire breaks out at one or more vertices of a graph, and at each time interval spreads to all neighbouring vertices that have not been protected earlier on. This is the general setup for The Firefighter Problem, which has attracted considerable attention since being introduced in 1995. We survey the directions and results that have been pursued, including algorithms and complexity, bounds, and containing the fire on infinite grids. The paper concludes with a collection of 26 open problems and possible research projects.

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