Graph classes: a survey
WG '98 Proceedings of the 24th International Workshop on Graph-Theoretic Concepts in Computer Science
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Approximation Algorithms for the Firefighter Problem: Cuts over Time and Submodularity
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximating the treewidth of AT-free graphs
Discrete Applied Mathematics
Resource minimization for fire containment
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Parameterized complexity of the firefighter problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Parameterized complexity of firefighting revisited
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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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 n1−ε for any ε0. 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 Pk-free graphs for fixed k. On the negative side, we show that the problem remains NP-hard on unit disk graphs.