An Optimal Algorithm for Preemptive On-line Scheduling

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.