On the Chvátal rank of polytopes in the 0/1 cube Original Research Article

Given a polytope P⊆Rn, the Chvátal–Gomory procedure computes iteratively the integer hull PI of P. The Chvátal rank of P is the minimal number of iterations needed to obtain PI. It is always finite, but already the Chvátal rank of polytopes in R2 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 Chvátal rank of any polytope P⊆[0,1]n is O(n3 log n) and prove the linear upper and lower bound n for the case P∩Zn=∅.