Combining Arithmetic and Geometric Rounding Techniques for Knapsack Problems

Abstract

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 faster polynomial time approximation scheme requiring only linear storage, that computes an approximate solution of any fixed accuracy in linear time. This linear complexity bound gives a substantial improvement of the best previously known polynomial bound [2].

Supported by the “Metaheuristics Network”, grant HPRN-CT-1999-00106, and by Swiss National Science Foundation project 21-55778.98, “Resource Allocation and Scheduling in Flexible Manufacturing Systems”.