The Packing Property

Abstract

A clutter (V;E) packs if the smallest number of vertices needed to intersect all the edges (i.e. a minumum transversal) is equal to the maximum number of pairwise disjoint edges (i.e. a maximum matching). This terminology is due to Seymour 1977. A clutter is minimally nonpacking if it does not pack but all its minors pack. An m n 0,1 matrix is minimally nonpacking if it is the edge-vertex incidence matrix of a minimally nonpacking clutter. Minimally nonpacking matrices can be viewed as the counterpart for the set covering problem of minimally imperfect matrices for the set packing problem. This paper proves several properties of minimally nonpacking clutters and matrices.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2000
Accession Number
AD1021247

Entities

People

  • Bertrand Guenin
  • Francois Margot
  • Gérard Cornuéjols

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Computer Programs
  • Computers
  • Construction
  • Coverings
  • Equations
  • Geometry
  • Identities
  • Inequalities
  • Integrals
  • Linear Systems
  • Mathematics
  • Permutations
  • Reproduction (Copying)
  • Structural Properties
  • Symmetry
  • Two Dimensional

Readers

  • Mathematical Modeling and Probability Theory.
  • Nanofabrication and Microfabrication.
  • Radar Systems Engineering.