## Abstract

We study the problem of scheduling n jobs that arrive over time. We consider a non-preemptive setting on a single machine. The goal is to minimize the total flow time. We use extra resource competitive analysis: an optimal off-line algorithm which schedules jobs on a single machine is compared to a more powerful on-line algorithm that has ℓ machines. We design an algorithm of competitive ratio O(min(Δ^{1/ℓ}, n^{1/ℓ})), where Δ is the maximum ratio between two job sizes, and provide a lower bound which shows that the algorithm is optimal up to a constant factor for any constant ℓ. The algorithm works for a hard version of the problem where the sizes of the smallest and the largest jobs are not known in advance, only Δ is known. This gives a trade-off between the resource augmentation and the competitive ratio. We also consider scheduling on parallel identical machines. In this case the optimal off-line algorithm has m machines and the on-line algorithm has ℓm machines. We give a lower bound for this case. Next, we give lower bounds for algorithms using resource augmentation on the speed. Finally, we consider scheduling with hard deadlines.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Rusins Freivalds |

Publisher | Springer Verlag |

Pages | 472-482 |

Number of pages | 11 |

ISBN (Print) | 9783540446699 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |

Event | 13th International Symposium on Fundamentals of Computation Theory, FCT 2001 - Riga, Latvia Duration: 22 Aug 2001 → 24 Aug 2001 |

### 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 | 2138 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 13th International Symposium on Fundamentals of Computation Theory, FCT 2001 |
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Country/Territory | Latvia |

City | Riga |

Period | 22/08/01 → 24/08/01 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2001.

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science