On the rank of mixed 0,1 polyhedra

On the rank of mixed 0,1 polyhedra

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Article ID: iaor2003740
Country: Germany
Volume: 91
Issue: 2
Start Page Number: 391
End Page Number: 397
Publication Date: Jan 2002
Journal: Mathematical Programming
Authors: ,
Keywords: programming: linear
Abstract:

For a polytope in the [0,1]n cube, Eisenbrand and Schulz showed recently that the maximum Chvátal rank is bounded above by O(n2logn) and bounded below by (1+ε)n for some ε > 0. Chvátal cuts are equivalent to Gomory fractional cuts, which are themselves dominated by Gomory mixed integer cuts. What do these upper and lower bounds become when the rank is defined relative to Gomory mixed integer cuts? An upper bound of n follows from existing results in the literature. In this note, we show that the lower bound is also equal to n. This result still holds for mixed 0,1 polyhedra with n binary variables.

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