## Abstract

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-∈)-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, online scheduling problem.

Original language | American English |
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Title of host publication | Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992 |

Publisher | Association for Computing Machinery |

Pages | 51-58 |

Number of pages | 8 |

ISBN (Electronic) | 0897915119 |

DOIs | |

State | Published - 1 Jul 1992 |

Externally published | Yes |

Event | 24th Annual ACM Symposium on Theory of Computing, STOC 1992 - Victoria, Canada Duration: 4 May 1992 → 6 May 1992 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F129722 |

ISSN (Print) | 0737-8017 |

### Conference

Conference | 24th Annual ACM Symposium on Theory of Computing, STOC 1992 |
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Country/Territory | Canada |

City | Victoria |

Period | 4/05/92 → 6/05/92 |

### Bibliographical note

Funding Information:The m-machine scheduling problem is one of the most widely-studied problems in computer science ([4, 5, 6, 7’J are surveys), with an almost limitless number of variants. For example, there can be precedence constraints *Computer Science Department, School of Mathematics, Tel-Aviv University, Tel-Aviv 69978, Israel. t Depwtment of Computer Science, University of Chicago. Earlier drafts of this paper were written while the author vie-ited DIMACS. This work supported in part by NSF grant CCR 9107349. $Department of Management Science, Ohio State university. This work supported in part by a Dean’s Research Professorship of the College of Business of the Ohio State University.

Publisher Copyright:

© 1992 ACM.