Advertisement

An Optimal Strategy for Online Non-uniform Length Order Scheduling

  • Feifeng Zheng
  • E. Zhang
  • Yinfeng Xu
  • Xiaoping Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)

Abstract

This paper will study an online non-uniform length order scheduling problem. For the case where online strategies have the knowledge of Δ beforehand, which is the ratio between the longest and shortest length of order, Ting [3] proved an upper bound of \((\frac{6\Delta}{\log\Delta}+O(\Delta^{5/6}))\) and Zheng et al. [2] proved a matching lower bound. This work will consider the scenario where online strategies do not have the knowledge of Δ at the beginning. Our main work is a \((\frac{6\Delta}{\log\Delta}+O(\Delta^{5/6}))\)-competitive optimal strategy, extending the result of Ting [3] to a more general scenery.

Keywords

Scheduling Online Strategy Competitive Ratio 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fung, S.P.Y., Chin, F.Y.L., Poon, C.K.: Laxity helps in broadcast scheduling. In: Proceedings of 11th Italian Conference on Theoretical Computer Science, Siena, Italy, pp. 251–264 (2005)Google Scholar
  2. 2.
    Zheng, F.F., Fung, S.P.Y., Chan, W.T., Chin, F.Y.L., Poon, C.K., Wong, P.W.H.: Improved On-line Broadcast Scheduling with Deadlines. In: Proceedings of the 12th Annual International Computing and Combinatorics Conference, Taipei, Taiwan, pp. 320–329 (2006)Google Scholar
  3. 3.
    Ting, H.F.: A near optimal scheduler for on-demand data broadcasts. In: 6th Italian Conference on Algorithms and Complexity, Rome, Italy, pp. 163–174 (2006)Google Scholar
  4. 4.
    Kim, J.H., Chwa, K.Y.: Scheduling broadcasts with deadlines. In: Proceedings of 9th Italian Conference on Theoretical Computer Science, Big Sky, MT, USA, pp. 415–424 (2003)Google Scholar
  5. 5.
    Zheng, F.F., Dai, W.Q., Xiao, P., Zhao, Y.: Competitive Strategies for On-line Production Order Disposal Problem. In: 1st International Conference on Algorithmic Applications In Management, Xi’an, China, pp. 46–54 (2005)Google Scholar
  6. 6.
    Borodin, A., El-yaniv, R.: Online computation and competitive analysis. Cambridge University Press, England (1998)zbMATHGoogle Scholar
  7. 7.
    Motwani, R., Phillips, S., Torng, E.: Nonclairvoyant Scheduling. Theoretical Computer Science 130(1), 17–47 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kalyanasundaram, B., Pruhs, K.R.: Minimizing flow time nonclairvoyantly. Journal of the ACM 50(4), 551–567 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Becchetti, L., Leonardi, S.: Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. Journal of the ACM 51(4), 517–539 (2004)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Lipton, R.J., Tomkins, A.: Online Interval Scheduling. In: Proc. Of the 5th Annual ACM-SIAM Symposium on Discrete Algorithm (SODA 1994), pp. 302–311. New York (1994)Google Scholar
  11. 11.
    Goldwasser, M.H.: Patience is a Virtue: The effect of slack on competitiveness for admission control. Journal of Scheduling 6(2), 183–211 (2003)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Feifeng Zheng
    • 1
  • E. Zhang
    • 2
  • Yinfeng Xu
    • 1
    • 3
  • Xiaoping Wu
    • 1
  1. 1.School of ManagementXi’an JiaoTong UniversityXi’anChina
  2. 2.School of Information Management and EngineeringShanghai University of Finance and EconomicsChina
  3. 3.The State Key Lab for Manufacturing Systems Engineering Xi’anChina

Personalised recommendations