Optimal Online Flow Time with Resource Augmentation

Abstract

We study the problem of scheduling n jobs that arrive over time. We consider a non-preemptive setting on a single machine. The goal is to minimize the total flow time. We use extra resource competitive analysis: an optimal off-line algorithm which schedules jobs on a single machine is compared to a more powerful on-line algorithm that has l machines. We design an algorithm of competitive ratio O(min(Δ^1/l, n ^1/l)), where Δ is the maximum ratio between two job sizes, and provide a lower bound which shows that the algorithm is optimal up to a constant factor for any constant l. The algorithm works for a hard version of the problem where the sizes of the smallest and the largest jobs are not known in advance, only Δ is known. This gives a trade-off between the resource augmentation and the competitive ratio.

We also consider scheduling on parallel identical machines. In this case the optimal off-line algorithm has m machines and the on-line algorithm has Im machines. We give a lower bound for this case. Next, we give lower bounds for algorithms using resource augmentation on the speed. Finally, we consider scheduling with hard deadlines.

Work carried out while the author was at Tel-Aviv University.

Research supported by the Netherlands Organization for Scientific Research (NWO), project number SION 612-30-002.