Abstract
We characterize when the intersection of a set-packing and a set-covering polyhedron or of their corresponding minors has a noninte- ger vertex. Our result is a common generalization of Lovász’s characteri- zation of ‘imperfect’ and Lehman’s characterization of ‘nonideal’ systems of inequalities, furthermore, it includes new cases in which both types of inequalities occur and interact in an essential way. The proof specializes to a conceptually simple and short common proof for the classical cases, moreover, a typical corollary extracting a new case is the following: if the intersection of a perfect and an ideal polyhedron has a noninteger. vertex, then they have minors whose intersection’s coefficient matrix is the incidentce matrix of an odd circuit graph.
Visiting the Research Institute for Mathematical Sciences, Kyoto University.
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Sebő, A. (1998). Characterizing Noninteger Polyhedra with 0–1 Constraints. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_4
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DOI: https://doi.org/10.1007/3-540-69346-7_4
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