On the rank of mixed 0,1 polyhedra |
| |
Authors: | Gérard Cornuéjols Yanjun Li |
| |
Affiliation: | (1) Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, USA, e-mail: gc0v@andrew.cmu.edu, US |
| |
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(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. Received: March 15, 2001 / Accepted: July 18, 2001?Published online September 17, 2001 |
| |
Keywords: | : mixed integer cut – disjunctive cut – split cut – rank – mixed 0,1 program |
本文献已被 SpringerLink 等数据库收录! |
|