A semidefinite programming relaxation for the generalized stable set problem

Tetsuya Fujie, Akihisa Tamura

研究成果: Article査読

抄録

In this paper, we generalize the theory of a convex set relaxation for the maximum weight stable set problem due to Grötschel, Lovász and Schrijver to the generalized stable set problem. We define a convex set which serves as a relaxation problem, and show that optimizing a lineal' function over the set can be done in polynomial time. This implies that the generalized stable set problem for perfect bidirected graphs is polynomial time solvable. Moreover, we prove that the convex set is a polytope if and only if the corresponding bidirected graph is perfect. The definition of the convex set is based on a semideflnite programming relaxation of Lovász and Schrijver for the maximum weight stable set problem, and the equivalent representation using infinitely many convex quadratic inequalities proposed by Fujie and Kojima is particularly important for our proof.

本文言語English
ページ(範囲)1122-1128
ページ数7
ジャーナルIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
E88-A
5
DOI
出版ステータスPublished - 2005

ASJC Scopus subject areas

  • 信号処理
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 電子工学および電気工学
  • 応用数学

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