Improved Approximation Algorithms for Firefighter Problem on Trees

Yutaka IWAIKAWA, Naoyuki KAMIYAMA, Tomomi MATSUI

Summary :

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.

• Publication: IEICE TRANSACTIONS on Information Vol.E94-D No.2 pp.196-199
• Publication Date: 2011/02/01
• Online ISSN: 1745-1361
• DOI: 10.1587/transinf.E94.D.196
• Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science -- Mathematical Foundations and Applications of Algorithms and Computer Science --)

Authors

Yutaka IWAIKAWA
Naoyuki KAMIYAMA
Tomomi MATSUI

Keyword

firefighter problem,  approximation algorithm,  rooted tree