Stable Sets, Corner Polyhedra and the Chvatal Closure

Abstract

In this work, we consider a classical formulation of the stable set problem. We characterize its corner polyhedron, i.e. the convex hull of the points satisfying all the constraints except the non-negativity of the basic variables. We show that the non-trivial inequalities necessary to describe this polyhedron can be derived from one row of the simplex tableau as fractional Gomory cuts. It follows in particular that the split closure is not stronger than the Chvatal closure for the stable set problem. The results are obtained via a characterization of the basis and its inverse in terms of a collection of connected components with at most one cycle.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2009
Accession Number
AD1021250

Entities

People

  • Gérard Cornuéjols
  • Manoel Campelo

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Coefficients
  • Commerce
  • Convex Sets
  • Decomposition
  • Equations
  • Identities
  • Inclusions
  • Inequalities
  • Integrals
  • Mathematics
  • Notation
  • Schools
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research