Abstract
In previous study on comparing the makespan of the schedule allowed to be preempted at most i times and that of the optimal schedule with unlimited number of preemptions, the worst case ratio was usually obtained by analyzing the structures of the optimal schedules. For m identical machines case, the worst case ratio was shown to be 2m/(m + i + 1) for any 0 ≤ i ≤ m − 1[1], and they showed that LPT algorithm is an exact algorithm which can guarantee the worst case ratio for i = 0. In this paper, we propose a simpler method which is based on the design and analysis of the algorithm and finding an instance in the worst case. It can obtain the worst case ratio as well as the algorithm which can guarantee this ratio for any 0 ≤ i ≤ m − 1, and thus we generalize the previous results. We also make a discussion on the trade-off between the objective value and the number of preemptions. In addition, we consider the i-preemptive scheduling on two uniform machines. For both i = 0 and i = 1, we present the algorithms and give the worst-case ratios with respect to s, i.e., the ratio of the speeds of two machines.
Supported by the National Natural Science Foundation of China (11001242, 11071220) and Zhejiang Province Natural Science Foundation of China (Y6090175, Y6090554).
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References
Braun, O., Schmidt, G.: Parallel processor scheduling with limited number of preemptions. SIAM Journal on Computing 32(3), 671–680 (2003)
Coffman Jr., E.G., Garey, M.R.: Proof of the 4/3 conjecture for preemptive vs. nonpreemptive two-processor scheduling. Journal of the Association for Computing Machinery 20, 991–1018 (1993)
Gonzalez, T., Sahni, S.: Preemptive scheduling of uniform processor systems. Journal of the Association for Computing Machinery 25, 92–101 (1978)
Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics 17, 416–429 (1969)
Horvath, E.C., Lam, S., Sethi, R.: A level algorithm for preemptive scheduling. Journal of the Association for Computing Machinery 24, 32–43 (1977)
Hong, K.S., Leung, J.Y.-T.: Some results on Lius conjecture. SIAM Journal on Discrete Mathematics 5, 500–523 (1992)
Liu, C.L.: Optimal scheduling on multi-processor computing systems. In: Proceedings of the 13th Annual Symposium on Switching and Automata Theory, pp. 155–160. IEEE Computer Society, Los Alamitos (1972)
McNaughton, R.: Scheduling with deadlines and loss functions. Management Science 6, 1–12 (1959)
Klonowska, K., Lundberg, L., Lennerstad, H.: The maximum gain of increasing the number of preemptions in multiprocessor scheduling. Acta Informatica 46, 285–295 (2009)
Liu, J.W.S., Yang, A.: Optimal scheduing of independent tasks on heterogeneous computing systems. In: Proceedings of ACM Annual Conference, San Diego, Cahf, pp. 38–45 (1974)
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Jiang, Y., Weng, Z., Hu, J. (2012). Algorithms with Limited Number of Preemptions for Scheduling on Parallel Machines. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29700-7_9
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DOI: https://doi.org/10.1007/978-3-642-29700-7_9
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