Online scheduling on uniform machines with two hierarchies

Authors:
Li-Ying Hou;Liying Kang
Affiliations:
Department of Mathematics, Nanjing Agricultural University, Nanjing, P.R. China 210095 and Department of Mathematics, Shanghai University, Shanghai, P.R. China 200444;Department of Mathematics, Shanghai University, Shanghai, P.R. China 200444
Venue:
Journal of Combinatorial Optimization
Year:
2012

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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 0sk=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.