An O(log m)-competitive algorithm for online machine minimization

Lin Chen, Nicole Megow, Kevin Schewior

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider the online machine minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a minimum number of machines. Our main result is a general O(log m)-competitive algorithm for the online problem, where m is the optimal number of machines used in an offline solution. This is the first improvement to an intriguing problem in nearly two decades. To date, the best known result is a O(log(pmax/p min ))-competitive algorithm by Phillips et al. [Optimal time-critical scheduling via resource augmentation, STOC, 1997] that depends on the ratio of maximum and minimum job sizes, pmax and pmin. Even for m = 2 no better algorithm was known. Our algorithm is in this case constant-competitive. When applied to laminar or agreeable instances, our algorithm achieves a competitive ratio of O(1) even independently of m. The following two key components lead to our new result. First, we derive a new lower bound on the optimum value that relates the laxity and the number of jobs with intersecting time windows. Then, we design a new algorithm that is tailored to this lower bound and balances the delay of jobs by taking the number of currently running jobs into account.

Original languageEnglish
Pages (from-to)2057-2077
Number of pages21
JournalSIAM Journal on Computing
Issue number6
StatePublished - 2018


  • Competitive analysis
  • Multiprocessor scheduling
  • Online algorithms


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