Abstract
In this paper, we study the online problem on three hierarchical machines with a buffer size of 1, and have two hierarchy, the objective is to minimize the maximum machine load. When there is only one low-hierarchy machine, we give a low bound \(\frac{3}{2}\) and present an online algorithm with competitive ratio at most \(\frac{5}{3}\). When there are two low-hierarchy machines, we give a lower bound \(\frac{3}{2}\) and present an online algorithm with competitive ratio at most \(\frac{12}{7}\).
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References
Hwang, H., Chang, S.Y., Lee, K.: Parallel machine scheduling under a grade of service provision. Comput. Oper. Res. 31(12), 2055–2061 (2004)
Ou, J., Leung, J.Y.T., Li, C.L.: Scheduling parallel machines with inclusive processing set restrictions. Nav. Res. Logist. 55(4), 328–338 (2008)
Li, W., Li, J., Zhang, T.: Two approximation schemes for scheduling on parallel machines under a grade of service provision. Asia Pac. J. Oper. Res. 29(05), 83–94 (2012)
Park, J., Chang, S.Y., Lee, K.: Online and semi-online scheduling of two machines under a grade of service provision. Oper. Res. Lett. 34(6), 692–696 (2006)
Jiang, Y., He, Y., Tang, C.: Optimal online algorithms for scheduling on two identical machines under a grade of service. J. Zhejiang Univ. Sci. A 7(3), 309–314 (2006)
Lim, K., Park, J., Chang, S.Y., Lee, K.: Online and semi-online scheduling of three machines under a GoS provision. In: Working Paper, Department of Industrial and Management Engineering, Pohang University of Science and Technology, Republic of Korea (2010)
Wu, Y., Ji, M., Yang, Q.: Optimal semi-online scheduling algorithm on two parallel identical machines under a grade of service provision. Int. J. Prod. Econ. 135(1), 367–371 (2012)
Zhang, A., Jiang, Y., Tan, Z.: Online parallel machines scheduling with two hierarchies. Theoret. Comput. Sci. 410(38), 3597–3605 (2009)
Zhang, A., Jiang, Y., Fan, L., Hu, J.: Optimal online algorithms on two hierarchical machines with tightly-grouped processing times. J. Comb. Optim. 29(4), 781–795 (2015)
Englert, M., Ozmen, D., Westermann, M.: The power of reordering for online minimum makespan scheduling. In: 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp. 603–612. IEEE (2008)
Lan, Y., Chen, X., Ding, N., Han, X.: Online minimum makespan scheduling with a buffer. In: Proceedings of the Joint International Conference on Frontiers in Algorithmics and Algorithmic Aspects in Information and Management, pp. 161–171 (2012)
Zhang, G.: A simple semi on-line algorithm for P2//\(C_{max}\) with a buffer. Inf. Process. Lett. 61(3), 145–148 (1997)
Chen, X., Xu, Z., Dosa, G., Han, X., Jiang, H.: Semi-online hierarchical scheduling problems with buffer or rearrangements. Inf. Process. Lett. 113(4), 127–131 (2013)
Li, J., Li, W., Li, J.: Polynomial approximation schemes for the max-min allocation problem under a grade of service provision. Discrete Math. Algorithms Appl. 1(03), 355–368 (2009)
Xiao, M., Wu, G., Li, W.: Semi-online machine covering on two hierarchical machines with known total size of low-hierarchy jobs. In: Sun, X., He, K., Chen, X. (eds.) NCTCS 2019. CCIS, vol. 1069, pp. 95–108. Springer, Singapore (2019). https://doi.org/10.1007/978-981-15-0105-0_7
Acknowledgements
The work is supported in part by the Program for Excellent Young Talents of Yunnan University, Training Program of National Science Fund for Distinguished Young Scholars, IRTSTYN, and Key Joint Project of the Science and Technology Department of Yunnan Province and Yunnan University [No. 2018FY001(-014)].
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Xiao, M., Ding, L., Zhao, S., Li, W. (2021). Semi-online Algorithms for Hierarchical Scheduling on Three Parallel Machines with a Buffer Size of 1. In: He, K., Zhong, C., Cai, Z., Yin, Y. (eds) Theoretical Computer Science. NCTCS 2020. Communications in Computer and Information Science, vol 1352. Springer, Singapore. https://doi.org/10.1007/978-981-16-1877-2_4
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DOI: https://doi.org/10.1007/978-981-16-1877-2_4
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