Preemptive online scheduling with reordering*

György Dósa, Leah Epstein

Research output: Contribution to journalArticlepeer-review


We consider online preemptive scheduling of jobs, arriving one by one, on m identical parallel machines. A buffer of a fixed size K > 0, which assists in partial reordering of the input, is available to be used for the storage of at most K unscheduled jobs. We study the effect of using a fixed-size buffer (of an arbitrary size) on the supremum competitive ratio over all numbers of machines (the overall competitive ratio), as well as the effect on the competitive ratio as a function of m. We find a tight bound on the competitive ratio for any m. This bound is 4/3 for even values of m and slightly lower for odd values of m. We show that a buffer of size Θ(m) is sufficient to achieve this bound, but using K = o(m) does not reduce the best overall competitive ratio that is known for the case without reordering, e/e-1 . We further consider the semionline variant where jobs arrive sorted by nonincreasing processing time requirements. In this case it turns out to be possible to achieve a competitive ratio of 1. In addition, we find tight bounds as a function of the buffer size and the number of machines for this semionline variant. Related results for nonpreemptive scheduling were recently obtained by Englert, Özmen, and Westermann.

Original languageEnglish
Pages (from-to)21-49
Number of pages29
JournalSIAM Journal on Discrete Mathematics
Issue number1
StatePublished - 2011


  • Buffer management
  • Online algorithms
  • Scheduling

ASJC Scopus subject areas

  • General Mathematics


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