Facets and lifting procedures for the set covering polytope
 Paolo Nobili,
 Antonio Sassano
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Given a family of subsetsℱ of an arbitrary groundsetE, acover ofℱ is any setC ⊂E having nonempty 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 nonBoolean facets of such a polytope. In Sections 5 and 6 we describe some nonsequential 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.
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 Title
 Facets and lifting procedures for the set covering polytope
 Journal

Mathematical Programming
Volume 45, Issue 13 , pp 111137
 Cover Date
 19890801
 DOI
 10.1007/BF01589100
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Independence systems
 set covering
 polytope
 facet
 Industry Sectors
 Authors

 Paolo Nobili ^{(1)}
 Antonio Sassano ^{(1)}
 Author Affiliations

 1. Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185, Roma, Italy