2011/04/06 by Ming Lam Leung, Leung, Ming Lam
Computer Science · Engineering · #Computational Geometry and Mesh Generation #Data Management and Algorithms #Data Structures and Algorithms (cs.DS) #Evacuation and Crowd Dynamics #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.1104.1044
14 pages, 5 figures
openalex publication_date 2011/04/06 · arxiv created 2011/04/08 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The firefighter problem is defined as below. A fire initially breaks out at a vertex r on a graph G. In each step, a firefighter chooses to protect one vertex, which is not yet burnt. And the fire spreads out to its unprotected neighboring vertices afterwards. The objective of the problem is to choose a sequence of vertices to protect, in order to save maximum number of vertices from the fire. In this paper, we will introduce a parameter k into the firefighter problem and give several FPT algorithms using a random separation technique of Cai, Chan and Chan. We will prove firefighter problem is FPT on general graph if we take total number of vertices burnt to be a parameter. If we parameterize the number of protected vertices, we discover several FPT algorithms of the firefighter problem on degree bounded graph and unicyclic graph. Furthermore, we also study the firefighter problem on weighted and valued graph, and the problem with multiple fire sources on degree-bounded graph.