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 mm/(mm - (m - 1)m) for every m 2, which increasingly tends to e/(e - 1) ˜ 1.58 as m ¿ 8. Moreover, we prove that for no m 2 there does exist any approximation algorithm with a better worst-case guarantee.