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.
Cite
@article{arxiv.0808.1119,
title = {Graham's Schedules and the Number Partition Problem},
author = {Seenu S. Reddi},
journal= {arXiv preprint arXiv:0808.1119},
year = {2008}
}