# 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

, Volume 28 (1) – Dec 13, 2011
6 pages

/lp/springer-journals/a-better-semi-online-algorithm-for-q3-s1-s2-s3-cmin-with-the-known-POTP2ZDPFE
Publisher
Springer Journals
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

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