Journal of Scheduling

, Volume 16, Issue 5, pp 461–477 | Cite as

Semi-online scheduling problems on a small number of machines

  • Kangbok Lee
  • Kyungkuk LimEmail author


We consider the semi-online parallel machine scheduling problem of minimizing the makespan given a priori information: the total processing time, the largest processing time, the combination of the previous two or the optimal makespan. We propose a new algorithm that can be applied to the problem with the known total or largest processing time and prove that it has improved competitive ratios for the cases with a small number of machines. Improved lower bounds of the competitive ratio are also provided by presenting adversary lower bound examples.


Semi-online scheduling Competitive ratio Lower bound example 


  1. Albers, S. (1999). Better bounds for online scheduling. SIAM Journal on Computing, 29, 459–473.CrossRefGoogle Scholar
  2. Albers, S., & Hellwig, M. (2012). Semi-online scheduling revisited. Theoretical Computer Science, 443, 1–9.CrossRefGoogle Scholar
  3. Angelelli, E., Nagy, A. B., Speranza, M. G., & Zs, Tuza. (2004). The on-line multiprocessor scheduling problem with known sum of the tasks. Journal of Scheduling, 7, 421–428.CrossRefGoogle Scholar
  4. Angelelli, E., Speranza, M. G., & Zs, Tuza. (2007). Semi on-line scheduling on three processors with known sum of the tasks. Journal of Scheduling, 10, 263–269.CrossRefGoogle Scholar
  5. Azar, Y., & Regev, O. (2001). On-line bin-stretching. Theoretical Computer Science, 268, 17–41.CrossRefGoogle Scholar
  6. Bartal, Y., Fiat, A., Karloff, H., & Vohra, R. (1995). New algorithms for an ancient scheduling problem. Journal of Computer and System Sciences, 51, 359–366.CrossRefGoogle Scholar
  7. Bartal, Y., Karloff, H., & Rabani, Y. (1994). A better lower bound for on-line scheduling. Information Processing Letters, 50, 113–116.CrossRefGoogle Scholar
  8. Cai, S. Y. (2002). Semi online scheduling on three identical machines. Journal of Wenzhou Teachers College, 23, 1–3. (In Chinese).Google Scholar
  9. Chang, S. Y., Hwang, H.-C., & Park, J. (2005). Semi-on-line parallel machines scheduling under known total and largest processing times. Journal of the Operations Research Society of Japan, 48, 1–8.Google Scholar
  10. Chen, B., Vliet, A., & Woeginger, G. J. (1994). New lower and upper bounds for on-line scheduling. Operations Research Letters, 16, 221–230.CrossRefGoogle Scholar
  11. Cheng, T. C. E., Kellerer, H., & Kotov, V. (2005). Semi-on-line multiprocessor scheduling with given total processing time. Theoretical Computer Science, 337, 134–146.CrossRefGoogle Scholar
  12. Faigle, U., Kern, W., & Turan, G. (1989). On the performance of on-line algorithms for partition problems. Acta Cybernetica, 9, 107–119.Google Scholar
  13. Fleischer, R., & Wahl, M. (2000). Online scheduling revisited. Journal of Scheduling, 3, 343–353.CrossRefGoogle Scholar
  14. Galambos, G., & Woeginger, G. J. (1993). An on-line scheduling heuristic with better worst case ratio than Graham’s list scheduling. SIAM Journal on Computing, 22, 349–355.CrossRefGoogle Scholar
  15. Graham, R. L. (1966). Bounds for certain multiprocessing anomalies. Bell System Technical Journal, 45, 1563–1581.CrossRefGoogle Scholar
  16. He, Y., & Zhang, G. C. (1999). Semi online scheduling on two identical machines. Computing, 62, 179–187.CrossRefGoogle Scholar
  17. Hua, R., Hu, J., & Lu, L. (2006). A semi-online algorithm for parallel machine scheduling on three machines. Journal of Industrial Engineering and, Engineering Management, 20 (in Chinese).Google Scholar
  18. Karger, D., Phillips, S., & Torng, E. (1996). A better algorithm for an ancient scheduling problem. Journal of Algorithms, 20, 400–430. Google Scholar
  19. Kellerer, H., Kotov, V., Speranza, M. G., & Tuza, Zs. (1997). Semi on-line algorithms for the partitioning problem. Operations Research Letters, 21, 235–242.CrossRefGoogle Scholar
  20. Rudin, J. F. (2001). Improved bounds for the on-line scheduling problem. Ph.D. Thesis, The University of Texas, Dallas.Google Scholar
  21. Rudin, J. F., & Chandrasekaran, R. (2003). Improved bounds for the online scheduling problem. SIAM Journal on Computing, 32, 717– 735.CrossRefGoogle Scholar
  22. Tan, Z. Y., & He, Y. (2002). Semi-on-line problems on two identical machines with combined partial information. Operations Research Letters, 30, 408–414.CrossRefGoogle Scholar
  23. Wu, Y., Huang, Y., & Yang, Q. F. (2008). Semi-online multiprocessor scheduling with the longest given processing time. Journal of Zhejiang University: Science Edition, 35, 23–26. (In Chinese).Google Scholar
  24. Wu, Y., Tan, Z., & Yang, Q. (2007). Optimal semi-online scheduling algorithms on a small number of machines. Lecture Notes in Computer Science, 4614, 504–515.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Supply Chain Management & Marketing SciencesRutgers Business SchoolNewarkUSA
  2. 2.BK21 ProjectSogang Business SchoolSeoulRepublic of Korea

Personalised recommendations