Facet of regular 0–1 polytopes
 P. L. Hammer,
 E. L. Johnson,
 U. N. Peled
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The role of 0–1 programming problems having monotone or regular feasible sets was pointed out in [6]. The solution sets of covering and of knapsack problems are examples of monotone and of regular sets respectively. Some connections are established between prime implicants of a monotone or a regular Boolean functionβ on the one hand, and facets of the convex hullH of the zeros ofβ on the other. In particular (Corollary 2) a necessary and sufficient condition is given for a constraint of a covering problem to be a facet of the corresponding integer polyhedron. For any prime implicantP ofβ, a nonempty familyF(P) of facets ofH is constructed. Proposition 17 gives easytodetermine sharp upper bounds for the coefficients of these facets whenβ is regular. A special class of prime implicants is described for regular functions and it is shown that for anyP in this class,F(P) consists of one facet ofH, and this facet has 0–1 coefficients. Every nontrivial facet ofH with 0–1 coefficients is obtained from this class.
 Title
 Facet of regular 0–1 polytopes
 Journal

Mathematical Programming
Volume 8, Issue 1 , pp 179206
 Cover Date
 197512
 DOI
 10.1007/BF01580442
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
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 Authors

 P. L. Hammer ^{(1)}
 E. L. Johnson ^{(2)}
 U. N. Peled ^{(1)}
 Author Affiliations

 1. University of Waterloo, Waterloo, Ontario, Cananda
 2. IBM Research, Yorktown Heights, N.Y., USA