Optimal semi-online algorithm for scheduling with rejection on two uniform machines

Authors:
Xiao Min;Jing Liu;Yuqing Wang
Affiliations:
Department of Mathematics and Information Engineering, Jiaxing College, Jiaxing, People's Republic of China 314001;Department of Mathematics and Information Engineering, Jiaxing College, Jiaxing, People's Republic of China 314001;Department of Mathematics and Information Engineering, Jiaxing College, Jiaxing, People's Republic of China 314001
Venue:
Journal of Combinatorial Optimization
Year:
2011

Citing 6
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Semi on-line algorithms for the partition problem

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Semi-online scheduling on two identical machines with rejection

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Abstract

In this paper we consider a semi-online scheduling problem with rejection on two uniform machines with speed 1 and s驴1, respectively. A sequence of independent jobs are given and each job is characterized by its size (processing time) and its penalty, in the sense that, jobs arrive one by one and can be either rejected by paying a certain penalty or assigned to some machine. No preemption is allowed. The objective is to minimize the sum of the makespan of schedule, which is yielded by all accepted jobs and the total penalties of all rejected ones. Further, two rejection strategies are permitted thus an algorithm can propose two different schemes, from which the better solution is chosen. For the above version, we present an optimal semi-online algorithm H that achieves a competitive ratio 驴 H (s) as a piecewise function in terms of the speed ratio s.