### Abstract

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.

Original language | English |
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Pages (from-to) | 194-204 |

Number of pages | 11 |

Journal | Journal of the Operations Research Society of Japan |

Volume | 44 |

Issue number | 2 |

Publication status | Published - 2001 Jun |

Externally published | Yes |

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### ASJC Scopus subject areas

- Decision Sciences(all)
- Management Science and Operations Research

### Cite this

*Journal of the Operations Research Society of Japan*,

*44*(2), 194-204.

**A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph.** / Nakamura, Daishin; Tamura, Akihisa.

Research output: Contribution to journal › Article

*Journal of the Operations Research Society of Japan*, vol. 44, no. 2, pp. 194-204.

}

TY - JOUR

T1 - A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph

AU - Nakamura, Daishin

AU - Tamura, Akihisa

PY - 2001/6

Y1 - 2001/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0038290871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038290871&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0038290871

VL - 44

SP - 194

EP - 204

JO - Journal of the Operations Research Society of Japan

JF - Journal of the Operations Research Society of Japan

SN - 0453-4514

IS - 2

ER -