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.

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U2 - 10.15807/jorsj.44.194

DO - 10.15807/jorsj.44.194

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 -