Mathematical Programming

, Volume 43, Issue 1, pp 45–55

On the 0, 1 facets of the set covering polytope

Authors

  • Gérard Cornuéjols
    • Graduate School of Industrial Administration Carnegie Mellon University
  • Antonio Sassano
    • Istituto di Analisi dei Sistemi ed Informatica del CNR Viale Manzoni 30
Article

DOI: 10.1007/BF01582277

Cite this article as:
Cornuéjols, G. & Sassano, A. Mathematical Programming (1989) 43: 45. doi:10.1007/BF01582277

Abstract

In this paper, we consider inequalities of the formΣ αjxj ≥ β, whereαj equals 0 or 1, andβ is a positive integer. We give necessary and sufficient conditions for such inequalities to define facets of the set covering polytope associated with a 0, 1 constraint matrixA. These conditions are in terms of critical edges and critical cutsets defined in the bipartite incidence graph ofA, and are in the spirit of the work of Balas and Zemel on the set packing problem where similar notions were defined in the intersection graph ofA. Furthermore, we give a polynomial characterization of a class of 0, 1 facets defined from chorded cycles of the bipartite incidence graph. This characterization also yields all the 0, 1 liftings of odd-hole inequalities for the simple plant location polytope.

Key words

Set coveringset packingpolytopefacetodd hole

Copyright information

© The Mathematical Programming Society, Inc. 1989