Task Distributions on Multiprocessor Systems

We consider the problem of scheduling of n independent jobs on m unrelated machines to minimize the max(t1, t2, ..., tm), ti being the completion time of machine i. In [1] was suggested a polynomial 2- approximation algorithm for this problem. It was also proved that there can exist no polynomial 1:5-approximation algorithm unless P = NP. Here we improve this earlier performance bound 2 to 2- 1/m. In [1] is also proved a general rounding theorem, which allows to construct in polynomial time 1-job approximations to the optimum, i.e. schedules with an absolute bound equal to the largest job processing time. We also improve this result and obtain (1 - 1/m)-job approximation to optimal.