Ideal polytopes and face structures of some combinatorial optimization problems

Yoshiko T. Ikebe, Akihisa Tamura

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Given a finite set X and a family of "feasible" subsets F of X, the 0-1 polytope P (F is defined as the convex hull of all the characteristic vectors of members of F We show that under a certain assumption a special type of face of P(F) is equivalent to the ideal polytope of some pseudo-ordered set. Examples of families satisfying the assumption are those related to the maximum stable set problem, set packing and set partitioning problems, and vertex coloring problem. Using this fact, we propose a new heuristic for such problems and give results of our preliminary computational experiments for the maximum stable set problem.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalMathematical Programming
Volume71
Issue number1
DOIs
Publication statusPublished - 1995 Nov
Externally publishedYes

Fingerprint

Combinatorial optimization
Coloring
Polytopes
Combinatorial Optimization Problem
Face
Stable Set
Polytope
Experiments
Set Packing
Set Partitioning
Vertex Coloring
Ordered Set
Convex Hull
Computational Experiments
Finite Set
Optimization problem
Stable set
Heuristics
Subset
Convex hull

Keywords

  • 0-1 polytopes
  • Heuristic
  • Ideal polytopes
  • Maximum stable set problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)
  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research
  • Software
  • Computer Graphics and Computer-Aided Design
  • Computer Science(all)

Cite this

Ideal polytopes and face structures of some combinatorial optimization problems. / Ikebe, Yoshiko T.; Tamura, Akihisa.

In: Mathematical Programming, Vol. 71, No. 1, 11.1995, p. 1-15.

Research output: Contribution to journalArticle

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