## Abstract

In this paper, we consider an ordinal on-line scheduling problem. A sequence of n independent jobs has to be assigned non-preemptively to two uniformly related machines. We study two objectives which are maximizing the minimum machine completion time, and minimizing the l_{p} norm of the completion times. It is assumed that the values of the processing times of jobs are unknown at the time of assignment. However it is known in advance that the processing times of arriving jobs are sorted in a non-increasing order. We are asked to construct an assignment of all jobs to the machines at time zero, by utilizing only ordinal data rather than actual magnitudes of jobs. For the problem of maximizing the minimum completion time we first present a comprehensive lower bound on the competitive ratio, which is a piecewise function of machine speed ratio s. Then, we propose an algorithm which is optimal for any s ≥ 1. For minimizing the l_{p} norm, we study the case of identical machines (s = 1) and present tight bounds as a function of p.

Original language | English |
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Pages (from-to) | 57-70 |

Number of pages | 14 |

Journal | Information and Computation |

Volume | 196 |

Issue number | 1 |

DOIs | |

State | Published - 2005 |

Externally published | Yes |

### Bibliographical note

Funding Information:∗ Corresponding author. E-mail addresses: tanzy@zju.edu.cn (Z. Tan), mathhey@zju.edu.cn (Y. He), lea@idc.ac.il (L. Epstein). 1 Research supported by the National Natural Science Foundation of China (10301028). 2 Research supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China, and National Natural Science Foundation of China (10271110, 60021201). 3 Research supported in part by Israel Science Foundation (Grant No. 250/01).

## Keywords

- Analysis of algorithm
- Competitive ratio
- Scheduling
- Semi-online

## ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Computer Science Applications
- Computational Theory and Mathematics