Graham's Schedules and the Number Partition Problem

Abstract

We show the equivalence of the Number Partition Problem and the two processor scheduling problem. We establish a priori bounds on the completion times for the scheduling problem which are tighter than Graham's but almost on par with a posteriori bounds of Coffman and Sethi. We conclude the paper with a characterization of the asymptotic behavior of the scheduling problem which relates to the spread of the processing times and the number of jobs.