Abstract
In this paper, we study the semi-online machine covering problem on two hierarchical machines, whose objective is to maximize the minimum machine load. When the processing times are discrete by \(\{1,2,2^{2},\ldots ,2^{k}\}\) with \(k\ge 2\), we prove that no algorithm can have a competitive ratio less than \(2^{k}\) and present an optimal semi-online algorithm with competitive ratio \(2^{k}\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Chassid, O., Epstein, L.: The hierarchical model for load balancing on two machines. J. Comb. Optim. 15(4), 305–314 (2008)
Hwang, H.C., Chang, S.Y., Lee, K.: Parallel machine scheduling under a grade of service provision. Comput. Oper. Res. 31(12), 2055–2061 (2004)
Jiang, Y., He, Y., Tang, C.: Optimal online algorithms for scheduling two identical machines under a grade of service. J. Zhejiang Univ. Sci. A. 7(3), 309–314 (2006)
Li, J., Li, W., Li, J.: Polynomial approximation schemes for the max-min allocation problem under a grade of service provision. Discret. Math. Algorithms Appl. 1(3), 355–368 (2009)
Luo, T., Xu, Y.: Semi-online hierarchical load balancing problem with bounded processing times. Theor. Comput. Sci. 607, 75–82 (2015)
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(5), Article No. 1250029 (2012)
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)
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)
Wu, Y., Cheng, T.C.E., Ji, M.: Optimal algorithm for semi-online machine covering on two hierarchical machines. Theor. Comput. Sci. 531, 37–46 (2014)
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., Fan, L., Hu, J.: Optimal online algorithms on two hierarchical machines with tightly-grouped processing times. J. Comb. Optim. 29(4), 781–795 (2015)
Acknowledgement
The work is supported in part by the National Natural Science Foundation of China [Nos. 11761078, 61662088], the Natural Science Foundation of Education Department of Yunnan Province [No. 2017ZZX235], IRTSTYN and Program for Excellent Young Talents, Yunnan University.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Wu, G., Li, W. (2018). Semi-online Machine Covering on Two Hierarchical Machines with Discrete Processing Times. In: Li, L., Lu, P., He, K. (eds) Theoretical Computer Science. NCTCS 2018. Communications in Computer and Information Science, vol 882. Springer, Singapore. https://doi.org/10.1007/978-981-13-2712-4_1
Download citation
DOI: https://doi.org/10.1007/978-981-13-2712-4_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2711-7
Online ISBN: 978-981-13-2712-4
eBook Packages: Computer ScienceComputer Science (R0)
