Online scheduling on three uniform machines

Authors:
Sheng-Yi Cai;Qi-Fan Yang
Affiliations:
School of Mathematics & Information Science, Wenzhou University, Wenzhou 325035, PR China and Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 3
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An On-Line Algorithm for Some Uniform Processor Scheduling

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A new algorithm for online uniform-machine scheduling to minimize the makespan

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Lower bounds for online makespan minimization on a small number of related machines

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Abstract

This paper investigates the online scheduling on three uniform machines problem. Denote by s"j the speed of each machine, j=1,2,3. Assume 0=3t5+2t-6t^2} and G"2={(s,t)|s(t-1)t=1+s,s=1,t=1}. The competitive ratio of LS is 1+s+2sts+st when (s,t)@?G"1 and 1+sst+1 when (s,t)@?G"2. Moreover, for the general speed ratios, we show the competitive ratio of LS is no more than min{1+s+2sts+st,1+sst+1,1+s+3st1+s+st} and its overall competitive ratio is 2 which matches the overall lower bound of the problem.