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The Firefighter Problem: A Structural Analysis

  • Janka Chlebíková
  • Morgan ChopinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)

Abstract

We consider the complexity of the firefighter problem where a budget of \({b \ge 1}\) firefighters are available at each time step. This problem is proved to be NP-complete even on trees of degree at most three and \({b = 1}\) [10] and on trees of bounded degree \(b+3\) for any fixed \(b \ge 2\) [3]. In this paper, we provide further insight into the complexity landscape of the problem by showing a complexity dichotomy result with respect to the parameters pathwidth and maximum degree of the input graph. More precisely, we first prove that the problem is NP-complete even on trees of pathwidth at most three for any \(b \ge 1\). Then we show that the problem turns out to be fixed parameter-tractable with respect to the combined parameter “pathwidth” and “maximum degree” of the input graph. Finally, we show that the problem remains NP-complete on very dense graphs, namely co-bipartite graphs, but is fixed-parameter tractable with respect to the parameter “cluster vertex deletion”.

Keywords

Maximum Degree Vertex Cover Input Graph Dense Graph Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University of PortsmouthSchool of ComputingPortsmouthUK
  2. 2.Institut für Optimierung und Operations ResearchUniversität UlmUlmGermany

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