Abstract
Given a polytope P⊆ R n , the Chvátal–Gomory procedure computes iteratively the integer hull P I of P. The Chvátal rank of P is the minimal number of iterations needed to obtain P I . It is always finite, but already the Chvátal rank of polytopes in R 2 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(n 3 log n) and prove the linear upper and lower bound n for the case P∩ Z n=∅ .
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