Some simplified NP-complete problems
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
The surviving rate of an infected network
Theoretical Computer Science
Surviving Rates of Graphs with Bounded Treewidth for the Firefighter Problem
SIAM Journal on Discrete Mathematics
The firefighter problem with more than one firefighter on trees
Discrete Applied Mathematics
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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 4k)-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.