Abstract
In this paper, we study three semi-online early work maximization problems on two hierarchical machines. When the total processing time of low or high hierarchy is known, we propose an optimal algorithm with a competitive ratio of \(\sqrt{5}-1\). When the total processing times of low and high hierarchy are known, we propose an optimal algorithm with a competitive ratio of \(\frac{6}{5}\).
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References
Chassid, O., Epstein, L.: The hierarchical model for load balancing on two machines. J. Comb. Optim. 15, 305–314 (2008)
Chen, X., Ding, N., Dosa, G., Han, X.: Online hierarchical scheduling on two machines with known total size of low-hierarchy jobs. Int. J. Comput. Math. 92(5), 873–881 (2015)
Chen, X., Kovalev, S., Liu, Y.Q., Sterna, M., Chalamon, I., Błażewicz, J.: Semi-online scheduling on two identical machines with a common due date to maximize total early work. Discret. Appl. Math. 290, 71–78 (2021)
Chen, X., Sterna, M., Han, X., Błażewicz, J.: Scheduling on parallel identical machines with late work criterion: offline and online cases. J. Sched. 19(6), 729–736 (2016)
Jiang, Y.W., He, Y., Tang, C.M.: Optimal online algorithms for scheduling on two identical machines under a grade of service. J. Zhejiang Univ. Sci. A 7, 309–314 (2006)
Luo, T.B., Xu, Y.F.: Semi-online scheduling on two machines with GoS levels and partial information of processing time. Sci. World J. 2, 576234 (2014)
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)
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
Xiao, M., Liu, X.Q., Li, W.D.: Online and semi-online scheduling on two hierarchical machines with a common due date to maximize total early work, working paper (2021)
Acknowledgement
The work is supported in part by the National Natural Science Foundation of China [No. 12071417], and Project for Innovation Team (Cultivation) of Yunnan Province [No. 202005AE160006].
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Xiao, M., Liu, X., Li, W. (2021). Semi-online Early Work Maximization Problem on Two Hierarchical Machines with Partial Information of Processing Time. In: Wu, W., Du, H. (eds) Algorithmic Aspects in Information and Management. AAIM 2021. Lecture Notes in Computer Science(), vol 13153. Springer, Cham. https://doi.org/10.1007/978-3-030-93176-6_13
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DOI: https://doi.org/10.1007/978-3-030-93176-6_13
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