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Making Life Easier for Firefighters

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7288)

Abstract

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.

Keywords

  • 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.

This work is supported by the Research Council of Norway and by the ERC StG project PAAl no. 259515.

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Fomin, F.V., Heggernes, P., van Leeuwen, E.J. (2012). Making Life Easier for Firefighters. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-30347-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30346-3

  • Online ISBN: 978-3-642-30347-0

  • eBook Packages: Computer ScienceComputer Science (R0)