An optimal algorithm for preemptive on-line scheduling

Abstract

We investigate the problem of on-line scheduling jobs on m identical parallel machines where preemption is allowed. The goal is to minimize the makespan. We derive an approximation algorithm with worst case guarantee m ^m/(m ^m −(m−1) ^m) for every m≥2, which increasingly tends to e/(e−1)≈1.58 as m→∞. Moreover, we prove that for no m≥2 there does exist any approximation algorithm with a better worst case guarantee.