neal young / Aslam99Improved

Two common objectives for evaluating a schedule are the makespan, or schedule length, and the average completion time. This short note gives improved bounds on the existence of schedules that simultaneously optimize both criteria. In particular, for any ρ > 0, there exists a schedule of makespan at most 1+ρ times the minimum, with average completion time at most 1/(1e^{ρ}) times the minimum. The proof uses an infinitedimensional linear program to generalize and strengthen a previous analysis by Cliff Stein and Joel Wein [1997].
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