Abstract
This paper studies online hierarchical scheduling on two uniform machines with the objective to minimize makespan. Machines are provided with different capability, i.e., the one with speed s can schedule all jobs, while the other one with speed 1 can only process partial jobs. Optimal algorithms for any 0<s<∞ are given in the paper. For 0<s<1, it has a competitive ratio of \(\min\{1+s,1+\frac{1+s}{1+s+s^{2}}\}\) . For s>1, the competitive ratio is \(\min\{\frac{1+s}{s},1+\frac{2s}{1+s+s^{2}}\}\) .
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Supported by the National Natural Science Foundation of China (10671177, 60021201) and Zhejiang Provincial Natural Science Foundation of China (Y607079).
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Tan, Z., Zhang, A. A note on hierarchical scheduling on two uniform machines. J Comb Optim 20, 85–95 (2010). https://doi.org/10.1007/s10878-008-9195-4
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DOI: https://doi.org/10.1007/s10878-008-9195-4