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On-line Access: 2024-08-27
Received: 2023-10-17
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Semi on-line scheduling for maximizing the minimum machine completion time on three uniform machines
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LUO Run-zi, SUN Shi-jie. Semi on-line scheduling for maximizing the minimum machine completion time on three uniform machines[J]. Journal of Zhejiang University Science A, 2005, 6(6): 591-595.
@article{title="Semi on-line scheduling for maximizing the minimum machine completion time on three uniform machines",
author="LUO Run-zi, SUN Shi-jie",
journal="Journal of Zhejiang University Science A",
volume="6",
number="6",
pages="591-595",
year="2005",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2005.A0591"
}
%0 Journal Article
%T Semi on-line scheduling for maximizing the minimum machine completion time on three uniform machines
%A LUO Run-zi
%A SUN Shi-jie
%J Journal of Zhejiang University SCIENCE A
%V 6
%N 6
%P 591-595
%@ 1673-565X
%D 2005
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2005.A0591
TY - JOUR
T1 - Semi on-line scheduling for maximizing the minimum machine completion time on three uniform machines
A1 - LUO Run-zi
A1 - SUN Shi-jie
J0 - Journal of Zhejiang University Science A
VL - 6
IS - 6
SP - 591
EP - 595
%@ 1673-565X
Y1 - 2005
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2005.A0591
Abstract: The paper investigates a semi on-line scheduling problem wherein the largest processing time of jobs done by three uniform machines M1, M2, M3 is known in advance. A speed si (s1=1, s2=r, s3=s, 1≤r≤s) is associated with machine Mi. Our goal is to maximize Cmin-the minimum workload of the three machines. We present a min3 algorithm and prove its competitive ratio is max{r+1,(3s+r+1)/(1+r+s)}, with the lower bound being at least max{2,r}. We also claim the competitive ratio of min3 algorithm cannot be improved and is the best possible for 1≤s≤2, r=1.
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