背包问题的混合舍入技术
Hybrid Rounding Techniques for Knapsack Problems
摘要：
我们解决经典的背包问题和一个变种，其中上限是强加的项目，可以选择的数量。我们表明，适当的舍入技术的组合产生新的和强大的舍入方式。作为这些技术的应用，我们提出了一个线性存储多项式时间近似方案（PTAS）和一个完全多项式时间近似方案（FPTAS），计算近似的解决方案，任何固定的精度，在线性时间。这个线性复杂性界给出了一个最好的以前已知的多项式界的实质性改进。
英文摘要：
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding. As an application of these techniques, we present a linear-storage Polynomial Time Approximation Scheme (PTAS) and a Fully Polynomial Time Approximation Scheme (FPTAS) that compute an approximate solution, of any fixed accuracy, in linear time. This linear complexity bound gives a substantial improvement of the best previously known polynomial bounds.
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