Mathematical Programming

, Volume 45, Issue 1, pp 1-20

First online:

On the set covering polytope: II. Lifting the facets with coefficients in {0, 1, 2}

  • Egon BalasAffiliated withCarnegie Mellon University
  • , Shu Ming NgAffiliated withUniversity of Southern California

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In an earlier paper (Mathematical Programming 43 (1989) 57–69) we characterized the class of facets of the set covering polytope defined by inequalities with coefficients equal to 0, 1 or 2. In this paper we connect that characterization to the theory of facet lifting. In particular, we introduce a family of lower dimensional polytopes and associated inequalities having only three nonzero coefficients, whose lifting yields all the valid inequalities in the above class, with the lifting coefficients given by closed form expressions.

Key words

Set covering facet lifting polyhedral combinatorics