The firefighter problem: Empirical results on random graphs

The firefighter problem is a deterministic discrete-time model for the spread and containment of fire on a graph. Once the fire breaks out at a set of vertices, the goal addressed in this work is to save as many vertices as possible from burning. Although the problem finds applications in various re...

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Bibliographic Details
Published in:Computers & operations research 2015-08, Vol.60, p.55-66
Main Authors: García-Martínez, C., Blum, C., Rodriguez, F.J., Lozano, M.
Format: Article
Language:English
Subjects:
Combustion
Communications networks
Containment
Diseases
Firefighter problem
Firefighters
Fires
Graph theory
Graphs
Heuristic
Heuristics
Integer linear programming techniques
Integer programming
Linear programming
Spreads
Strategy
Studies
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Summary:The firefighter problem is a deterministic discrete-time model for the spread and containment of fire on a graph. Once the fire breaks out at a set of vertices, the goal addressed in this work is to save as many vertices as possible from burning. Although the problem finds applications in various real-world problems, such as the spread of diseases or hoaxes contention in communication networks, this problem has not been addressed from a practical point of view so far, in the sense of finding a good strategy for the general case. In this work, we develop and compare several integer linear programming techniques and heuristic methods. Random graphs are used for the purpose of comparison. The obtained results shed some light on the challenges for computational tools as caused by graph topology, graph size, and the number of firefighters per iteration, when looking for the best strategy for an a priori unknown graph.
ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2015.02.004