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A valid inequality \alpha^Tx \ge \alpha_0 for a set covering problem is saidto have pitch <= k ( a positive integer) if the k smallest positive \alpha_jsum to at least alpha_0. This paper presents a new, simple derivation of arelaxation for set covering problems whose solutions satisfy all validinequalities of pitch and is of polynomial size, for each fixed . We alsoconsider the minimum knapsack problem, and show that for each fixed integer p >0 and 0 < \epsilon < 1 one can separate, within additive tolerance \epsilon,from the relaxation defined by the valid inequalities with coefficients in {0,1, . . . , p} in time polynomial in the number of variables and 1/\epsilon.

Simpler derivation of bounded pitch inequalities for set covering, and minimum knapsack sets