On the 0, 1 facets of the set covering polytope
 Gérard Cornuéjols,
 Antonio Sassano
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In this paper, we consider inequalities of the formΣ α _{j}x_{j} ≥ β, whereα _{j} 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 oddhole inequalities for the simple plant location polytope.
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 Title
 On the 0, 1 facets of the set covering polytope
 Journal

Mathematical Programming
Volume 43, Issue 13 , pp 4555
 Cover Date
 19890101
 DOI
 10.1007/BF01582277
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Set covering
 set packing
 polytope
 facet
 odd hole
 Industry Sectors
 Authors

 Gérard Cornuéjols ^{(1)}
 Antonio Sassano ^{(2)}
 Author Affiliations

 1. Graduate School of Industrial Administration Carnegie Mellon University, 15213, Pittsburgh, PA, USA
 2. Istituto di Analisi dei Sistemi ed Informatica del CNR Viale Manzoni 30, 00185, Roma, Italy