Mathematical Programming

, Volume 45, Issue 1, pp 111–137

Facets and lifting procedures for the set covering polytope

  • Paolo Nobili
  • Antonio Sassano
Article

DOI: 10.1007/BF01589100

Cite this article as:
Nobili, P. & Sassano, A. Mathematical Programming (1989) 45: 111. doi:10.1007/BF01589100

Abstract

Given a family of subsets of an arbitrary groundsetE, acover of is any setCE having non-empty intersection with every subset inℱ.

In this paper we deal with thecovering polytope, i.e., the convex hull of the incidence vectors of all the covers ofℱ. In Section 2 we review all the known properties of the covering polytope. In Sections 3 and 4 we introduce two new classes of non-Boolean facets of such a polytope. In Sections 5 and 6 we describe some non-sequential lifting procedures. In Section 7 a generalization of the notion ofweb introduced by L.E. Trotter is presented together with the facets of the covering polytope produced by such a structure.

Moreover, the strong connections between several combinatorial problems and the covering problem are pointed out and, exploiting those connections, some examples are presented of new facets for the Knapsack and Acyclic Subdigraph polytopes.

Key words

Independence systemsset coveringpolytopefacet

Copyright information

© North-Holland 1989

Authors and Affiliations

  • Paolo Nobili
    • 1
  • Antonio Sassano
    • 1
  1. 1.Istituto di Analisi dei Sistemi ed Informatica del CNRRomaItaly