## Abstract

We consider the on-line load balancing problem where there are m identical machines (servers). Jobs arrive at arbitrary times, where each job has a weight and a duration. A job has to be assigned upon its arrival to exactly one of the machines. The duration of each job becomes known only upon its termination (this is called temporary tasks of unknown durations). Once a job has been assigned to a machine it cannot be reassigned to another machine. The goal is to minimize the maximum over time of the sum (over all machines) of the squares of the loads, instead of the traditional maximum load. Minimizing the sum of the squares is equivalent to minimizing the load vector with respect to the ℓ_{2} norm. We show that for the ℓ_{2} norm greedy algorithm performs within at most 1.50 of the optimum. We show (an asymptotic) lower bound of 1.33 on the competitive ratio of the greedy algorithm. We also show a lower bound of 1.20 on the competitive ratio of any deterministic algorithm. We extend our techniques and analyze the competitive ratio of greedy with respect to the ℓ_{p} norm. We show that the greedy algorithm performs within at most 2 - Ω(1/p) of the optimum. We also show a lower bound of 2 - O(lnp/p) on the competitive ratio of any on-line algorithm.

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 | Klaus Jansen, Roberto Solis-Oba |

Publisher | Springer Verlag |

Pages | 53-66 |

Number of pages | 14 |

ISBN (Electronic) | 3540210792, 9783540210795 |

DOIs | |

State | Published - 2004 |

Externally published | Yes |

### 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 | 2909 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science

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