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Parallel machine covering with limited number of preemptions

Applied Mathematics(A Journal of Chinese Universities) 2014年第1期29卷 18-28页

作者： JIANG Yi-wei HU Jue-liang WENG Ze-wei ZHU Yu-qing Department of Mathematics Zhejiang Sci-Tech University Department of Computer Science The University of Texas at Dallas

In this paper, we investigate the/-preemptive scheduling on parallel machines to maximize the minimum machine completion time, i.e., machine covering problem with limited number of preemptions. It is aimed to obtain the worst case ratio of the objective value of the optimal schedule with unlimited preemptions and that of the schedule allowed to be preempted at most i times. For the m identical machines case, we show the worst case ratio is 2m-i-1/m and we present a polynomial time algorithm which can guarantee the ratio for any 0 〈 i 〈2 m - 1. For the /-preemptive scheduling on two uniform machines case, we only need to consider the cases of i = 0 and i = 1. For both cases, we present two linear time algorithms and obtain the worst case ratios with respect to s, i.e., the ratio of the speeds of two machines.

关键词： 90B35 90C27 68Q25 i-preemptive scheduling machine covering approximation algorithm worst case ratio

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A Better Semi-online Algorithm for Q3/s_1=s_2≤s_3/C_(min) with the Known Largest Size

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Acta Mathematicae Applicatae Sinica 2012年第1期28卷 111-116页

作者： Sheng-yi CAI Qi-fan YANG Department of Mathematics Zhejiang UniversityHangzhou 310027China School of Mathematics&Information Science Wenzhou UniversityWenzhou 325035China

This paper investigates the semi-online machine covering problem on three special uniform machines with the known largest size. Denote by sj the speed of each machine, j = 1, 2, 3. Assume 0 〈 s1 = s2 = r 〈 t = s3, and let s = t/r be the speed ratio. An algorithm with competitive ratio max（2, 3s＋6/s＋6 is presented. We also show the lower bound is at least max（2, 38 3s/s＋6）. For s ≤ 6, the algorithm is an optimal algorithm with the competitive ratio 2. Besides, its overall competitive ratio is 3 which matches the overall lower bound. The algorithm and the lower bound in this paper improve the results of Luo and Sun.

关键词： analysis of algorithms scheduling machine covering semi-online competitive ratio

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