On the Chvátal Rank of Polytopes in the 0/1 Cube

Given a polytope P⊆Rn, the Chv atal–Gomory procedure computes iteratively the integer hull PI of P. The Chv atal rank of P is the minimal number of iterations needed to obtain PI . It is always nite, but already the Chv atal rank of polytopes in R can be arbitrarily large. In this paper, we study polytopes in the 0=1 cube, which are of particular interest in combinatorial optimization. We show that the Chv atal rank of any polytope P⊆ [0; 1] is O(n log n) and prove the linear upper and lower bound n for the case P ∩Zn= ∅. ? 1999 Elsevier Science B.V. All rights reserved.