Worst Case Analysis of Two Scheduling Algorithms

• Published in: SIAM journal on computing Vol. 6; no. 3; pp. 518 - 536
• Main Authors: Lam, Shui, Sethi, Ravi
• Format: Journal Article
• Language: English; Japanese
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.09.1977
• Subjects: Algorithms; Critical path; Job shops; Schedules; Scheduling
• ISSN: 0097-5397; 1095-7111
• DOI: 10.1137/0206037

Coffman and Graham give an algorithm to schedule unit execution time task systems nonpreemptively. On two processors, their algorithm is optimal. We show that in general, if $\omega$ is the length of a schedule produced by their algorithm and $\omega_0$ the length of an optimal schedule, then $\omega / \omega_{0} \leqq 2 - 2/m$, where $m$ is the number of processors. The preemptive equivalent of the above algorithm has been considered by Muntz and Coffman. Again we show that the ratio of the lengths of theirs and an optimal schedule is bounded by $2 - 2/m$. In both the nonpreemptive and the preemptive cases there exist task systems for which the ratio $2 - 2/m$ can be approached arbitrarily closely. On a small number of machines, $2 - 2/m$ is not too far from 1. In particular, as noted above, on two machines the ratio is 1.