论文信息 - On the Chvátal Rank of Polytopes in the 0/1 Cube

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

Abstract Given a polytope P⊆ R n , the Chvatal–Gomory procedure computes iteratively the integer hull PI of P. The Chvatal rank of P is the minimal number of iterations needed to obtain PI. It is always finite, but already the Chvatal 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 Chvatal 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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