Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data

Zhiyi Tan; Yong He; Leah Epstein

doi:10.1016/j.ic.2004.10.002

Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data

Zhiyi Tan, Yong He, Leah Epstein

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	57-70
Number of pages	14
Journal	Information and Computation
Volume	196
Issue number	1
DOIs	https://doi.org/10.1016/j.ic.2004.10.002
State	Published - 2005
Externally published	Yes

Bibliographical note

Funding Information:
∗ Corresponding author. E-mail addresses: [email protected] (Z. Tan), [email protected] (Y. He), [email protected] (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

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10.1016/j.ic.2004.10.002

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title = "Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data",

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 lp 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 lp norm, we study the case of identical machines (s = 1) and present tight bounds as a function of p.",

keywords = "Analysis of algorithm, Competitive ratio, Scheduling, Semi-online",

author = "Zhiyi Tan and Yong He and Leah Epstein",

note = "Funding Information: ∗ Corresponding author. E-mail addresses: [email protected] (Z. Tan), [email protected] (Y. He), [email protected] (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).",

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doi = "10.1016/j.ic.2004.10.002",

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PY - 2005

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N2 - 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 lp 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 lp norm, we study the case of identical machines (s = 1) and present tight bounds as a function of p.

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Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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