Politician's firefighting

Abstract

Firefighting is a combinatorial optimization problem on graphs that models the problem of determining the optimal strategy to contain a fire and save as much from the fire as possible. We introduce and study a new version of firefighting, Politician's Firefighting, which exhibits more locality than the classical one-firefighter version. We prove that this locality allows us to develop an O(bn)-time algorithm on trees, where b is the number of nodes initially on fire. We further prove that Politician's Firefighting is NP-hard on planar graphs of degree at most 5. We present an O(m+ k2.5 4 k)-time algorithm for this problem on general graphs, where k is the number of nodes that burn using the optimal strategy, thereby proving that it is fixed-parameter tractable. We present experimental results that show that our algorithm's search-tree size is in practice much smaller than the worst-case bound of 4k. © 2006 Springer-Verlag Berlin/Heidelberg.