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

65 引用 (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.

元の言語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
発行部数2
出版物ステータスPublished - 2001 6
外部発表Yes

Fingerprint

Stable set
Graph
Polynomial-time algorithm
NP-hard
Polynomials

ASJC Scopus subject areas

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

これを引用

@article{ab9d1765752149e3a5e87c3790d0a020,
title = "A revision of Minty's algorithm for finding a maximum weight stable set of a claw-free graph",
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 Lov{\'a}sz 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.",
author = "Daishin Nakamura and Akihisa Tamura",
year = "2001",
month = "6",
language = "English",
volume = "44",
pages = "194--204",
journal = "Journal of the Operations Research Society of Japan",
issn = "0453-4514",
publisher = "Operations Research Society of Japan",
number = "2",

}

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 -