Abstract
In this paper we study online scheduling problem on m parallel uniform machines with two hierarchies. The objective is to minimize the maximum completion time (makespan). Machines are provided with different capability. The machines with speed s can schedule all jobs, while the other machines with speed 1 can only process partial jobs. Online algorithms for any 0<s<∞ are provided in the paper. For the case of k=1 and m=2, and the case of some values of s, k=1 and m=3, the algorithms are the best possible, where k is the number of machines with hierarchy 1, and m is the number of machines. Lower bounds for some special cases are also presented.
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Research was partially supported by the National Nature Science Foundation of China (No. 10971131) and Shanghai Leading Academic Discipline Project (No. S30104).
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Hou, Ly., Kang, L. Online scheduling on uniform machines with two hierarchies. J Comb Optim 24, 593–612 (2012). https://doi.org/10.1007/s10878-011-9410-6
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DOI: https://doi.org/10.1007/s10878-011-9410-6