论文标题
用于涵盖线性程序及其应用于bin包装的近似算法
An Approximation Algorithm for Covering Linear Programs and its Application to Bin-Packing
论文作者
论文摘要
假设存在$（1/α）$ - 近似算法，我们给出了$α（1+ε）$ - 近似算法，用于某些优化问题。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$α（1+ε）$ - 大约解决了一类大型bin包装问题的配置LP，假设存在$（1/α）$ - 相应的指背问题（KS）的近似算法（KS）。先前的结果为我们提供了配置LP的PTA，使用KS的PTA。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$α$。
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 $α$.
