New algorithms for an ancient scheduling problem

Yair Bartal, Amos Fiat, Howard Karloff, Rakesh Vohra

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


We consider the on-line version of the original m-machine scheduling problem: given m machines and n positive real jobs, schedule the n jobs on the m machines so as to minimize the makespan, the completion time of the last job. In the on-line version, as soon as job j arrives, it must be assigned immediately to one of the m machines. We present two main results. The first is a (2 - ε)-competitive deterministic algorithm for all m. The competitive ratio of all previous algorithms approaches 2 as m → ∞. Indeed, the problem of improving the competitive ratio for large m had been open since 1966, when the first algorithm for this problem appeared. The second result is an optimal randomized algorithm for the case m = 2. To the best of our knowledge, our 4/3-competitive algorithm is the first specifically randomized algorithm for the original, m-machine, on-line scheduling problem.

Original languageAmerican English
Pages (from-to)359-366
Number of pages8
JournalJournal of Computer and System Sciences
Issue number3
StatePublished - Dec 1995
Externally publishedYes


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