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 greater than or equal to 2, which increasingly tends to e/(e - 1) approximate to 1.58 as m --> infinity. Moreover, we prove that for no m greater than or equal to 2 there does exist any approximation algorithm with a better worst-case guarantee.