Abstract
In this paper, we consider the on-line scheduling of unit time jobs with rejection on m identical parallel machines. The objective is to minimize the total completion time of the accepted jobs plus the total penalty of the rejected jobs. We give an on-line algorithm for the problem with competitive ratio \(\frac{1}{2}(2+\sqrt{3})\approx{1.86602}\).
Similar content being viewed by others
References
Y. Bartal, S. Leonardi, A. Marchetti-Spaccamela, J. Sgall, and L. Stougie, Multiprocessor scheduling with rejection, SIAM J. Discrete Math., 2000, 13: 64–78.
S. S. Seiden, Preemptive multiprocessor scheduling with rejection, Theoret. Comput. Sci., 2001, 262: 437–458.
Hoogeveen, M. Skutella, and G. J. Woeginger, Preemptive scheduling with rejection, in Proceedings of the Eighth European Symposium on Algorithms (ESA’2000), Lecture Notes in Computers Science, Springer, Berlin, 2000, 1879: 268–277.
D. W. Engels, D. R. Karger, S. G. Kolliopoulos, S. Sengupta, R. N. Uma, and J. Wein, Techniques for scheduling with rejection, in Proceedings of the Sixth European Symposium on Algorithms (ESA’1998), Lecture Notes in Computer Science, Springer, Berlin, 1998, 1461: 490–501.
Leah Epstein, Join Noga, and Gerhard J. Woeginger, On-line scheduling of unit time with rejection: Minimizing the total completion time, Operations Research Letters, 2002, 30: 415–420.
Xiaotie Deng, Chung Keung Poon, and Yuzhong Zhang, Approximation algorithms in batch processing, J. Comb. Optim., 2003, 7(3): 247–257.
Xiaotie Deng, Haodi Feng, Pixing Zhang, Yuzhong Zhang, and Hong Zhu, Minimizing mean completion time in a batch processing system, Algorithmica, 2004, 38(4): 513–528.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by Natural Science Foundation of China under Grant No. 10171054.
Rights and permissions
About this article
Cite this article
Miao, C., Zhang, Y. On-Line Scheduling with Rejection on Identical Parallel Machines. Jrl Syst Sci & Complex 19, 431–435 (2006). https://doi.org/10.1007/s11424-006-0431-7
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s11424-006-0431-7