### Abstract

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 NPhard 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 (1 - 1/e)- approximation algorithm, we obtain (1- k-1/(k-1)e+1 )-approximation algorithm when a root has k children. In case of ternary trees, k ≥ 3 and thus the approximation ratio satisfies (1 - k-1/(k-1)e+1 ) ≥ 0.6892, which improves the existing result 1 - 1/e ≥ 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 (1-1/e)-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.

Original language | English |
---|---|

Pages (from-to) | 196-199 |

Number of pages | 4 |

Journal | IEICE Transactions on Information and Systems |

Volume | E94-D |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2011 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Hardware and Architecture
- Computer Vision and Pattern Recognition
- Electrical and Electronic Engineering
- Artificial Intelligence

### Cite this

*IEICE Transactions on Information and Systems*,

*E94-D*(2), 196-199. https://doi.org/10.1587/transinf.E94.D.196

**Improved approximation algorithms for firefighter problem on trees.** / Iwaikawa, Yutakaa; Kamiyama, Naoyuki; Matsui, Tomomi.

Research output: Contribution to journal › Article

*IEICE Transactions on Information and Systems*, vol. E94-D, no. 2, pp. 196-199. https://doi.org/10.1587/transinf.E94.D.196

}

TY - JOUR

T1 - Improved approximation algorithms for firefighter problem on trees

AU - Iwaikawa, Yutakaa

AU - Kamiyama, Naoyuki

AU - Matsui, Tomomi

PY - 2011/2

Y1 - 2011/2

N2 - 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 NPhard 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 (1 - 1/e)- approximation algorithm, we obtain (1- k-1/(k-1)e+1 )-approximation algorithm when a root has k children. In case of ternary trees, k ≥ 3 and thus the approximation ratio satisfies (1 - k-1/(k-1)e+1 ) ≥ 0.6892, which improves the existing result 1 - 1/e ≥ 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 (1-1/e)-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.

AB - 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 NPhard 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 (1 - 1/e)- approximation algorithm, we obtain (1- k-1/(k-1)e+1 )-approximation algorithm when a root has k children. In case of ternary trees, k ≥ 3 and thus the approximation ratio satisfies (1 - k-1/(k-1)e+1 ) ≥ 0.6892, which improves the existing result 1 - 1/e ≥ 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 (1-1/e)-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.

UR - http://www.scopus.com/inward/record.url?scp=79951507164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951507164&partnerID=8YFLogxK

U2 - 10.1587/transinf.E94.D.196

DO - 10.1587/transinf.E94.D.196

M3 - Article

AN - SCOPUS:79951507164

VL - E94-D

SP - 196

EP - 199

JO - IEICE Transactions on Information and Systems

JF - IEICE Transactions on Information and Systems

SN - 0916-8532

IS - 2

ER -