### Abstract

In this paper, we consider the prize-collecting edge dominating set problem, which is a generalization of the edge dominating set problem. In the prize-collecting edge dominating set problem, we are not forced to dominate all edges, but we need to pay penalties for edges which are not dominated. It is known that this problem is script N P-hard, and Parekh presented a 8/3-approximation algorithm. To the best of our knowledge, no polynomial-time solvable case is known for this problem. In this paper, we show that the prize-collecting edge dominating set problem in trees can be solved in polynomial time.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 2010 - 35th International Symposium, MFCS 2010, Proceedings |

Pages | 465-476 |

Number of pages | 12 |

DOIs | |

Publication status | Published - Nov 22 2010 |

Externally published | Yes |

Event | 35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010 - Brno, Czech Republic Duration: Aug 23 2010 → Aug 27 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6281 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010 |
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Country | Czech Republic |

City | Brno |

Period | 8/23/10 → 8/27/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Mathematical Foundations of Computer Science 2010 - 35th International Symposium, MFCS 2010, Proceedings*(pp. 465-476). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6281 LNCS). https://doi.org/10.1007/978-3-642-15155-2_41

**The prize-collecting edge dominating set problem in trees.** / Kamiyama, Naoyuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Foundations of Computer Science 2010 - 35th International Symposium, MFCS 2010, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6281 LNCS, pp. 465-476, 35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010, Brno, Czech Republic, 8/23/10. https://doi.org/10.1007/978-3-642-15155-2_41

}

TY - GEN

T1 - The prize-collecting edge dominating set problem in trees

AU - Kamiyama, Naoyuki

PY - 2010/11/22

Y1 - 2010/11/22

N2 - In this paper, we consider the prize-collecting edge dominating set problem, which is a generalization of the edge dominating set problem. In the prize-collecting edge dominating set problem, we are not forced to dominate all edges, but we need to pay penalties for edges which are not dominated. It is known that this problem is script N P-hard, and Parekh presented a 8/3-approximation algorithm. To the best of our knowledge, no polynomial-time solvable case is known for this problem. In this paper, we show that the prize-collecting edge dominating set problem in trees can be solved in polynomial time.

AB - In this paper, we consider the prize-collecting edge dominating set problem, which is a generalization of the edge dominating set problem. In the prize-collecting edge dominating set problem, we are not forced to dominate all edges, but we need to pay penalties for edges which are not dominated. It is known that this problem is script N P-hard, and Parekh presented a 8/3-approximation algorithm. To the best of our knowledge, no polynomial-time solvable case is known for this problem. In this paper, we show that the prize-collecting edge dominating set problem in trees can be solved in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=78349297517&partnerID=8YFLogxK

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U2 - 10.1007/978-3-642-15155-2_41

DO - 10.1007/978-3-642-15155-2_41

M3 - Conference contribution

SN - 364215154X

SN - 9783642151545

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 465

EP - 476

BT - Mathematical Foundations of Computer Science 2010 - 35th International Symposium, MFCS 2010, Proceedings

ER -