On the rank of mixed 0,1 polyhedra

For a polytope in the [0,1]ⁿ cube, Eisenbrand and Schulz showed recently that the maximum Chvátal rank is bounded above by O(n ²logn) 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.

Authors and Affiliations

1. Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, USA, e-mail: gc0v@andrew.cmu.edu, , , , , , US

   Gérard Cornuéjols & Yanjun Li

Received: March 15, 2001 / Accepted: July 18, 2001¶Published online September 17, 2001

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