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+ k 2.5 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.
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© 2006 Springer-Verlag Berlin Heidelberg
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Scott, A.E., Stege, U., Zeh, N. (2006). Politician’s Firefighting. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_61
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DOI: https://doi.org/10.1007/11940128_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49694-6
Online ISBN: 978-3-540-49696-0
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