Semi-online scheduling with known maximum job size on two uniform machines

Authors:
Qian Cao;Zhaohui Liu
Affiliations:
Department of Mathematics, East China University of Science and Technology, Shanghai, China 200237;Department of Mathematics, East China University of Science and Technology, Shanghai, China 200237
Venue:
Journal of Combinatorial Optimization
Year:
2010

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Abstract

In this paper, we investigate the semi-online scheduling problem with known maximum job size on two uniform machines with the speed ratio s驴1. The objective is to minimize the makespan. Two algorithms are presented, where the first is optimal for $1\leq s\leq\sqrt{2}$ , and the second is optimal for 1.559驴s驴2 and $s\ge \frac{3+\sqrt{17}}{2}$ . In addition, the improvement on lower bounds is made for $2 .