Resource augmentation in load balancing

Yossi Azar, Leah Epstein, Rob Van Stee

Research output: Contribution to journalArticlepeer-review


We consider load balancing in the following setting. The on-line algorithm is allowed to use n machines, whereas the optimal off-line algorithm is limited to m machines, for some fixed m<n. We show that while the greedy algorithm has a competitive ratio which decays linearly in the inverse of n/m, the best on-line algorithm has a ratio which decays exponentially in n/m. Specifically, we give a deterministic algorithm with competitive ratio of 1 +2-n/m(1-0(1)), and a lower bound of 1 + e-(n/m)(1+0(1)) on the competitive ratio of any randomized algorithm. We also consider the preemptive case. We show an on-line algorithm with a competitive ratio of 1 + e-(n/m)(1+0(1)). We show that the algorithm is optimal by proving a matching lower bound. We also consider the non-preemptive model with temporary tasks. We prove that for n = m +1, the greedy algorithm is optimal. (It is not optimal for permanent tasks.)

Original languageEnglish
Pages (from-to)249-258
Number of pages10
JournalJournal of Scheduling
Issue number5
StatePublished - 2000
Externally publishedYes


  • Competitive ratio
  • Load balancing
  • On-line

ASJC Scopus subject areas

  • Software
  • Engineering (all)
  • Management Science and Operations Research
  • Artificial Intelligence


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