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On the 0,1 facets of the set covering polytope. (English) Zbl 0675.90054
Necessary and sufficient conditions for an inequality with 0-1 coefficients to define a facet of the set covering polytope associated with the 0-1 constraint matrix A are given. The work is influenced by the results on the set packing problem, where also the notations are defined in the intersection graph of A. For the case that A is a matrix of odd order and the matrix $H contains exactly two ones per row and per column it is shown how to decide in polynomial time whether ${\sum }_{j=1}^{n}{x}_{j}>\left(n+1\right)/2$ is valid. This yields a facet of the set covering polytope.
Reviewer: N.Yanev
##### MSC:
 90C09 Boolean programming 52Bxx Polytopes and polyhedra 05C70 Factorization, etc. 90C35 Programming involving graphs or networks 90C10 Integer programming
##### Keywords:
facet; set covering polytope; set packing; intersection graph
##### References:
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