A polynomial approximation scheme for machine scheduling on uniform processors: Using the dual approximation approach

Abstract

In this paper we present a polynomial approximation scheme for the minimum makespan problem on uniform parallel processors. More specifically, the problem is to find a schedule for a set of independent jobs on a collection of machines of different speeds so that the last job to finish is completed as quickly as possible. We give a family of polynomial-time algorithms {Aϵ} such that Aϵ delivers a solution that is within a relative error of ϵ of the optimum. The technique employed is the dual approximation approach, where infeasible but superoptimal solutions for a related (dual) problem are converted to the desired feasible but possibly suboptimal solution.