Making Life Easier for Firefighters

  • Fedor V. Fomin
  • Pinar Heggernes
  • Erik Jan van Leeuwen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)


Being a firefighter is a tough job, especially when tight city budgets do not allow enough firefighters to be on duty when a fire starts. This is formalized in the Firefighter problem, which aims to save as many vertices of a graph as possible from a fire that starts in a vertex and spreads through the graph. In every time step, a single additional firefighter may be placed on a vertex, and the fire advances to each vertex in its neighborhood that is not protected by a firefighter. The problem is notoriously hard: it is NP-hard even when the input graph is a bipartite graph or a tree of maximum degree 3, it is W[1]-hard when parameterized by the number of saved vertices, and it is NP-hard to approximate within n 1 − ε for any ε > 0. We aim to simplify the task of a firefighter by providing algorithms that show him/her how to efficiently fight fires in certain types of networks. We show that Firefighter can be solved in polynomial time on various well-known graph classes, including interval graphs, split graphs, permutation graphs, and P k -free graphs for fixed k. On the negative side, we show that the problem remains NP-hard on unit disk graphs.


Optimal Strategy Bipartite Graph Interval Graph Input Graph Graph Class 
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-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Pinar Heggernes
    • 1
  • Erik Jan van Leeuwen
    • 2
  1. 1.Department of InformaticsUniversity of BergenNorway
  2. 2.Dept. Computer and System SciencesUniversity of Rome “La Sapienza”Italy

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