A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph

Daishin Nakamura, Akihisa Tamura

研究成果: Article査読

74 被引用数 (Scopus)

抄録

The maximum weight/cardinality stable set problem is to find a maximum weight/cardinality stable set of a given graph. It is well known that these problems for general graphs belong to the class of NP-hard. However, for several classes of graphs, e.g., for perfect graphs and claw-free graphs and so on, these problems can be solved in polynomial time. For instance, Minty (1980), Sbihi (1980) and Lovász and Plummer (1986) have proposed polynomial time algorithm finding a maximum cardinality stable set of a claw-free graph. Moreover, it has been believed that Minty's algorithm is the unique polynomial time algorithms finding a maximum weight stable set of a claw-free graph up to date. Here we show that Minty's algorithm for the weighted version fails for some special cases, and give modifications to overcome it.

本文言語English
ページ(範囲)194-204
ページ数11
ジャーナルJournal of the Operations Research Society of Japan
44
2
DOI
出版ステータスPublished - 2001 6
外部発表はい

ASJC Scopus subject areas

  • 決定科学(全般)
  • 経営科学およびオペレーションズ リサーチ

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