Graham's Schedules and the Number Partition Problem

TL;DR

This paper demonstrates the equivalence between the Number Partition Problem and a two-processor scheduling problem, providing tighter bounds on completion times and analyzing their asymptotic behavior based on processing time spread and job count.

Contribution

It establishes a formal equivalence between the Number Partition Problem and two-processor scheduling, and derives new bounds and asymptotic characterizations for scheduling performance.

Findings

Equivalence between Number Partition and two-processor scheduling

Tighter a priori bounds on completion times

Asymptotic behavior related to processing time spread and job number

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.