Non-preemptive scheduling of n independent jobs on m unrelated machines so as to minimize the maximal job completion time is considered. A polynomial algorithm with the worst-case absolute error of min{(1 − 1/m) pmax>, p′max} is presented, where pmax is the largest job processing time and p′max is the mth element from the non-increasing list of job processing times. This is better than the earlier known best absolute error of pmax. The algorithm is based on the rounding of acyclic multiprocessor distributions. An O(nm2) algorithm for the construction of an acyclic multiprocessor distribution is also presented.
