Minimum-cost b-Edge dominating sets on trees

Takehiro Ito, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Yoshio Okamoto

研究成果: Chapter

1 被引用数 (Scopus)

抄録

We consider the minimum-cost b-edge dominating set problem. This is a generalization of the edge dominating set problem, but the computational complexity for trees is an astonishing open problem. We make steps toward the resolution of this open problem in the following three directions. (1) We give the first combinatorial polynomial-time algorithm for paths. Prior to our work, the polynomial-time algorithm for paths used linear programming, and it was known that the linearprogramming approach could not be extended to trees. Thus, our algorithm would yield an alternative approach to a possible polynomial-time algorithm for trees. (2) We give a fixed-parameter algorithm for trees with the number of leaves as a parameter. Thus, a possible NP-hardness proof for trees should make use of trees with unbounded number of leaves. (3) We give a fully polynomial-time approximation scheme for trees. Prior to our work, the best known approximation factor was two. If the problem is NP-hard, then a possible proof cannot be done via a gap-preserving reduction from any APX-hard problem unless P = NP.

本文言語English
ホスト出版物のタイトルAlgorithms and Computation - 25th International Symposium, ISAAC 2014, Proceedings
編集者Hee-Kap Ahn, Chan-Su Shin
出版社Springer Verlag
ページ195-207
ページ数13
ISBN(電子版)9783319130743
DOI
出版ステータスPublished - 2014

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
8889
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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