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A better semi-online algorithm for Q3/s1 = s2≤ s3/Cmin with the known largest size

A better semi-online algorithm for Q3/s1 = s2≤ s3/Cmin with the known largest size This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by s j the speed of each machine, j = 1, 2, 3. Assume 0 < s 1 = s 2 = r ≤ t = s 3, and let s = t/r be the speed ratio. An algorithm with competitive ratio $$\max \left\{ {2,\tfrac{{3s + 6}} {{s + 6}}} \right\}$$ is presented. We also show the lower bound is at least $$\max \left\{ {2,\tfrac{{3s}} {{s + 6}}} \right\}$$ . For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A better semi-online algorithm for Q3/s1 = s2≤ s3/Cmin with the known largest size

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics; Applications of Mathematics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0137-7
Publisher site
See Article on Publisher Site

Abstract

This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by s j the speed of each machine, j = 1, 2, 3. Assume 0 < s 1 = s 2 = r ≤ t = s 3, and let s = t/r be the speed ratio. An algorithm with competitive ratio $$\max \left\{ {2,\tfrac{{3s + 6}} {{s + 6}}} \right\}$$ is presented. We also show the lower bound is at least $$\max \left\{ {2,\tfrac{{3s}} {{s + 6}}} \right\}$$ . For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Dec 13, 2011

References