A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach

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 {A} such that A delivers a solution that is within a relative error e of the optimum. This is a dramatic improvement over previously known algorithms; the best performance guarantee previously proved for a polynomial-time algorithm ensured a relative error no more than 40 percent. 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. 1. Introduction. We will consider a fundamental problem of scheduling theory. Suppose that we have a set of jobs J with independent processing times p,..., Pn