Improved Approximation Algorithms for Firefighter Problem on Trees

Yutaka IWAIKAWA  Naoyuki KAMIYAMA  Tomomi MATSUI  

IEICE TRANSACTIONS on Information and Systems   Vol.E94-D   No.2   pp.196-199
Publication Date: 2011/02/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E94.D.196
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science -- Mathematical Foundations and Applications of Algorithms and Computer Science --)
firefighter problem,  approximation algorithm,  rooted tree,  

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The firefighter problem is used to model the spread of fire, infectious diseases, and computer viruses. This paper deals with firefighter problem on rooted trees. It is known that the firefighter problem is NP-hard even for rooted trees of maximum degree 3. We propose techniques to improve a given approximation algorithm. First, we introduce an implicit enumeration technique. By applying the technique to existing ()-approximation algorithm, we obtain -approximation algorithm when a root has k children. In case of ternary trees, k=3 and thus the approximation ratio satisfies ≥ 0.6892, which improves the existing result ≥ 0.6321. Second technique is based on backward induction and improves an approximation algorithm for firefighter problem on ternary trees. If we apply the technique to existing () -approximation algorithm, we obtain 0.6976-approximation algorithm. Lastly, we combine the above two techniques and obtain 0.7144-approximation algorithm for firefighter problem on ternary trees.