Approximation Algorithms for the Knapsack Problem

Abstract

Approximation algorithms and in particular approximation schemes like PTAS and FPTAS were already introduced in Section 2.5 and 2.6, respectively. The main motivation in these sections was to illustrate the basic concept of constructing simple approximation schemes. The focus was put on algorithms where both the correctness and the required complexities were easy to understand without having to go deeply into the details of complicated technical constructions. Hence, an intuitive understanding about the basic features of approximation should have been brought to the reader which is a necessary prerequisite to tackle the more sophisticated methods required to improve upon the performance of these simple algorithms.