## Abstract

We consider the on-line problem of scheduling jobs with precedence constraints on m machines. We concentrate in two models, the model of uniformly related machines and the model of restricted assignment. For the related machines model, we show a lower bound of Ω (√ m) for deterministic and randomized on-line algorithms, with or without preemptions even for jobs of known durations. This matches the deterministic upper bound of O(√ m) given by Jaffe for task sys-tems. The lower bound should be contrasted with the known bounds for jobs without precedence constraints. Specifically, without precedence constraints, if we allow preemptions then the competitive ratio becomes θ(logm), and if the durations of the jobs are known then there are O(1) competitive (preemptive and non-preemptive) algorithms. We also consider the restricted assignment model. For the model with consistent precedence constraints, we give a (randomized) lower bound of Ω (logm) with or without preemptions. We show that the (deterministic) greedy algorithm (no preemptions used), is optimal for this model i.e. O(logm) competitive. However, for general precedence constraints, we show a lower bound of m which is easily matched by a greedy algorithm.

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 | 164-174 |

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
- Computer Science (all)