We give an $\alpha(1+\epsilon)$-approximation algorithm for solving covering LPs, assuming the presence of a $(1/\alpha)$-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 $\alpha(1+\epsilon)$-approximately solve the configuration LP for a large class of bin-packing problems, assuming the presence of a $(1/\alpha)$-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 $\alpha$.

中文翻译：

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覆盖线性程序的近似算法及其在装箱中的应用

我们给出了用于解决覆盖LP的$ \ alpha（1+ \ epsilon）$逼近算法，假设存在针对某个优化问题的$（1 / \ alpha）$逼近算法。我们的算法基于对Plotkin-Shmoys-Tardos算法的简单修改（MOR 1995）。然后，我们将算法应用于$ \ alpha（1+ \ epsilon）$-近似解决一类大型装箱问题的配置LP，并假定存在（$ 1/1 / alpha）$近似算法。相应的背包问题（KS）。先前的结果使用KS的PTAS为我们提供了配置LP的PTAS。这些结果不会扩展到KS近似差的情况。但是，我们的算法甚至适用于多项式大的$ \ alpha $。