Randomized on-line scheduling on two uniform machines

Leah Epstein, John Noga, Steve Seiden, Jiří Sgall, Gerhard Woeginger

Research output: Contribution to journalArticlepeer-review


We study the problem of on-line scheduling on two uniform machines with speeds 1 and s ≥ 1. A φ ≈ 1.61803 competitive deterministic algorithm was already known. We present the first randomized results for this problem: We show that randomization does not help for speeds s ≥ 2, but does help for all s < 2. We present a simple memoryless randomized algorithm with competitive ratio (4 - s)(1 + s)/4 ≤ 1.56250. We analyse other randomized algorithms that demonstrate that the randomized competitive ratio is at most 1.52778 for any s. These algorithms are barely random, i.e. they use only a constant number of random bits. Finally, we present a 1 + s/(s2 + s + 1) competitive deterministic algorithm for the preemptive version of this problem. For any s, it is best possible even among randomized preemptive algorithms.

Original languageEnglish
Pages (from-to)71-92
Number of pages22
JournalJournal of Scheduling
Issue number2
StatePublished - 2001
Externally publishedYes


  • Analysis of algorithms
  • Competitive ratio
  • On-line algorithms
  • Scheduling

ASJC Scopus subject areas

  • Software
  • General Engineering
  • Management Science and Operations Research
  • Artificial Intelligence


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