Parameterized complexity of the firefighter problem

Authors:
Cristina Bazgan;Morgan Chopin;Michael R. Fellows
Affiliations:
LAMSADE, Université Paris-Dauphine, France;LAMSADE, Université Paris-Dauphine, France;Charles Darwin University, Australia
Venue:
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Year:
2011

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Abstract

In this paper we study the parameterized complexity of the firefighter problem. More precisely, we show that Savingk-Vertices and its dual Saving All Butk-Vertices are both W[1]-hard for parameter k even for bipartite graphs. We also investigate several cases for which the firefighter problem is tractable. For instance, Savingk-Vertices is fixed-parameter tractable on planar graphs for parameter k. Moreover, we prove a lower bound to polynomial kernelization for Saving All Butk-Vertices.