Existence theorems, lower bounds and algorithms for scheduling to meet two objectives

Authors:
April Rasala;Cliff Stein;Eric Torng;Patchrawat Uthaisombut
Affiliations:
MIT Laboratory for Computer Science, Cambridge, MA;Columbia University, New York, NY;Michigan State University, East Lansing, MI;University of Pittsburgh, Pittsburgh, PA
Venue:
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2002

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Abstract

We give general results about the existence of schedules which simultaneously minimize two criteria. Our results are general in that (i) they apply to any scheduling environment and (ii) they apply to all pairs of metrics in which the first metric is one of maximum flow time, makespan, or maximum lateness and the second metric is one of average flow time, average completion time, average lateness, or number of on-time jobs. For most of the pairs of metrics we consider, we show the existence of near-optimal schedules for both metrics as well as some lower bound results. For some pairs of metrics such as (maximum flow time, average weighted flow time) and (maximum flow time, number of on-time jobs), we prove negative results on the ability to approximate both criteria within a constant factor of optimal. For many other criteria we present lower bounds that match or approach our bicriterion existence results.