Hybrid rounding techniques for knapsack problems

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 [2].

• Type: Journal
• Year: 2006
• Where: DAM
• Authors: Monaldo Mastrolilli, Marcus Hutter
• Keywords: DAM 2006, Fully Polynomial Time Approximation Scheme, Linear-storage Polynomial Time, Polynomial Time Approximation Scheme