Fully Polynomial Approximation Schemes for Decomposable Partition Problems

Abstract

A partition type extremum problem (problem PT_ext) is formulated. It is assumed that the objective function of this problem can be represented as a composition of some auxiliary functions which can recursively be computed. Properties of the problem PT_ext are established which are sufficient for developing a fully polynomial approximation scheme (FPAS) for this problem. Such a scheme is described. Several known discrete optimization and scheduling problems can be formulated in terms of the problem PT_ext. The suggested approach provides original FPASes for some problems, generalizes several exisiting FPASes and gives clear exposition of their main ideas.