Total dual integrality and integer polyhedra |
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Authors: | F.R. Giles W.R. Pulleyblank |
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Affiliation: | Department of Operations Research Cornell University Ithaca, New York, USA;CORE, de Croylaan 54 3030 Heverlee Belgium |
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Abstract: | A linear system Ax ? b (A, b rational) is said to be totally dual integral (TDI) if for any integer objective function c such that max {cx: Ax ? b} exists, there is an integer optimum dual solution. We show that if P is a polytope all of whose vertices are integer valued, then it is the solution set of a TDI system Ax ? b where b is integer valued. This was shown by Edmonds and Giles [4] to be a sufficient condition for a polytope to have integer vertices. |
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