An Approximation Algorithm for Covering Linear Programs and its Application to Bin-Packing
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We give an α(1+ϵ)-approximation algorithm for solving covering LPs, assuming the presence of a (1/α)-approximation algorithm for a certain optimization problem. Our algorithm is based on a simple modification of the Plotkin-Shmoys-Tardos algorithm (MOR 1995). We then apply our algorithm to α(1+ϵ)-approximately solve the configuration LP for a large class of bin-packing problems, assuming the presence of a (1/α)-approximate algorithm for the corresponding knapsack problem (KS). Previous results give us a PTAS for the configuration LP using a PTAS for KS. Those results don't extend to the case where KS is poorly approximated. Our algorithm, however, works even for polynomially-large α.
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