## Abstract

Weconsider the following non-preemptive semi-online scheduling problem. Jobs with non-increasing sizes arrive one by one to be scheduled on two uniformly related machines, with the goal of minimizing the makespan. We analyze both the optimal overall competitive ratio, and the optimal competitive ratio as a function of the speed ratio (q ≥ 1) between the two machines. We show that the greedy algorithm LPT has optimal competitive ratio ¼ (1 + √17) ≈ 1.28 overall, but does not have optimal competitive ratio for every value of q. Wedetermine the intervals of q where LPT is an algorithm of optimal competitive ratio, and design different algorithms of optimal competitive ratio for the intervals where it fails to be the best algorithm. As a result, we give a tight analysis of the competitive ratio for every speed ratio.

Original language | English |
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Title of host publication | Mathematical Foundations of Computer Science 2002 - 27th International Symposium, MFCS 2002, Proceedings |

Editors | Krzysztof Diks, Wojciech Rytter, Wojciech Rytter |

Publisher | Springer Verlag |

Pages | 245-256 |

Number of pages | 12 |

ISBN (Print) | 3540440402, 9783540440406 |

DOIs | |

State | Published - 2002 |

Externally published | Yes |

Event | 27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002 - Warsaw, Poland Duration: 26 Aug 2002 → 30 Aug 2002 |

### 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 | 2420 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 27th International Symposium on Mathematical Foundations of Computer Science, MFCS 2002 |
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Country/Territory | Poland |

City | Warsaw |

Period | 26/08/02 → 30/08/02 |

### Bibliographical note

Funding Information:– The research of Lene M. Favrholdt was supported in part by the Danish Natural Sci-ence Research Council (SNF) and in part by the Future and Emerging Technologies program of the EU under contract number IST-1999-14186 (ALCOM-FT).

Funding Information:

– The research of Leah Epstein was supported in part by the Israel Science Foundation, (grant no. 250/01).

Publisher Copyright:

© Springer-Verlag Berlin Heidelberg 2002.

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)