Optimal on-line flow time with resource augmentation

Leah Epstein, Rob Van Stee

Research output: Contribution to journalArticlepeer-review


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 1+2min(Δ1/ℓ,n1/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 and n are 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 ℓm 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, and scheduling so as to minimize the total completion time.

Original languageEnglish
Pages (from-to)611-621
Number of pages11
JournalDiscrete Applied Mathematics
Issue number4
StatePublished - 15 Mar 2006


  • Flow time
  • On-line algorithms
  • Resource augmentation
  • Scheduling

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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