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How good are sparse cuts

for some linear function c ∈ Zn . One way to solve (1) is to apply standard linear programming algorithms that receive as input an outer description of P , that is, a finite set of linear inequalities whose set of feasible solution is exactly P . Sometimes this description can be very “ugly”, either because the number of inequalities is very big, or because the coefficients of the inequalities have a big encoding length. A natural question is then how good we can approximate (1) if we only use inequalities valid for P that belong to a prescribed family F . The paper [1] investigate this problem when F is the set of all k−sparse cuts, that is, inequalities with at most k coefficients different from 0. Let P k be the approximation of P obtained using k-sparse cuts valid for P , and define