Computer Science – Computational Complexity
Scientific paper
2003-05-02
Discrete Applied Mathematics, 154:4 (2006) 640-649
Computer Science
Computational Complexity
19 LaTeX pages
Scientific paper
10.1016/j.dam.2005.08.004
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.
Hutter Marcus
Mastrolilli Monaldo
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