An EPTAS for scheduling jobs on uniform processors: Using an MILP relaxation with a constant number of integral variables

Abstract

In this paper, we present an efficient polynomial time approximation scheme (EPTAS) for scheduling on uniform processors, i.e. finding a minimum length schedule for a set of n independent jobs on m processors with different speeds (a fundamental NP-hard scheduling problem). The previous best polynomial time approximation scheme (PTAS) by Hochbaum and Shmoys has a running time of . Our algorithm, based on a new mixed integer linear programming (MILP) formulation with a constant number of integral variables and an interesting rounding method, finds a schedule whose length is within a relative error ε of the optimum, and has running time . © 2009 Springer Berlin Heidelberg.