## Abstract

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 ffixed 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 an algorithm with competitive ratio of 1 + 1/2^{n/m(1−o(1))}, and a lower bound of 1 + 1/e^{n/m(1+o(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 + 1=e^{n/m(1+o(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 language | English |
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Title of host publication | Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings |

Editors | Magnús M. Halldórsson |

Publisher | Springer Verlag |

Pages | 189-199 |

Number of pages | 11 |

ISBN (Print) | 3540676902, 9783540676904 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

Event | 7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway Duration: 5 Jul 2000 → 7 Jul 2000 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1851 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 |
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Country/Territory | Norway |

City | Bergen |

Period | 5/07/00 → 7/07/00 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2000.

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science