Advertisement

Journal of Global Optimization

, Volume 27, Issue 1, pp 97–103 | Cite as

Competitive Analysis of a Better On-line Algorithm to Minimize Total Completion Time on a Single-machine

  • Jairo R. Montoya-Torres
Article

Abstract

We consider the problem of scheduling jobs on-line on a single machine with the objective of minimizing total completion time. We assume that jobs arrive over time and that release dates are known in advance, but not the processing times. The most important result we are given in this paper is the competitive analysis of a new clairvoyant on-line algorithm for this scheduling problem. We are proving that this deterministic semi-online algorithm, called ST-α, is \(\sqrt 3\)-competitive, which beats the existing lower bound for non-clairvoyant online algorithms.

competitive analysis completion time on-line scheduling single-machine 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Azar, Y. and Regev, O. (1998), Online bin stretching. In Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science, Barcelona, Spain.Google Scholar
  2. Chekuri, C., Motwani, R., Natarajan, B. and Stein, C. (1997), Approximation techniques for average completion time scheduling. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA.Google Scholar
  3. Conway, R., Maxwell, W. and Miller, L.W. (1967), Theory of Scheduling. Addison-Wesley, Reading, MA.Google Scholar
  4. Goemnas, M.X., Queyranne, M., Schulz, A., Skutella, M. and Wang, Y (2002). Single machine scheduling with release dates, Journal on Discrete Mathematics 15, 65-192.Google Scholar
  5. Hall, L.A., Schulz, A., Shmoys, D.B. and Wein, J. (1997), Scheduling to minimize average completion time: off-line and on-line approximation algorithms, Mathematics of Operations Research 22, 513-544.Google Scholar
  6. Hoogeveen, J.A. and Vestjens, A.P.A. (1996), Optimal on-line algorithms for single-machine scheduling. In: Cunningham, W.H., McCornick, S.T. and Queyranne, M. (Eds.), Integer Programming and Combinatorial Optimization, Springer, Berlin.Google Scholar
  7. Kellerer, H., Kotov, V., Speranza M. and Tuza, Z. (1997), Semi-online algorithms for the partition problem. Operations Research Letters 21, 235-242.Google Scholar
  8. Lenstra, J.K, Rinnooy Kan, A.H.G. and Brucker, P. (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics 1, 343-362.Google Scholar
  9. Liu, W.P., Sidney, J.B. and van Vliet, A. (1996). Ordinal algorithms for parallel machine scheduling. Operations Research Letters 18, 223-232.Google Scholar
  10. Lu, X. Sitters, R., and Stougie, L. (2002). A class of on-line scheduling algorithms to minimize total completion time. 10 th European Symposium on Algorithms. Rome, Italy, Submitted.Google Scholar
  11. Montoya Torres, J.R. (2002), Une etude de l'influence de l'information anticipee en ordonnancement dynamique. Master's thesis. Institut National Polytechnique de Grenoble, France.Google Scholar
  12. Motwani, R., Phillips, S. and Torng, E. (1994). Non-clairvoyant scheduling. Theoretical Computer Science 130, 17-47.Google Scholar
  13. Phillips, C., Stein, C. and Wein, J. (1995). Minimizing average completion time in the presence of release dates. Mathematical Programming 82, 199-223.Google Scholar
  14. Schrage, L.E. (1968). A proof of the optimality of the shortest remaining processing time discipline, Operations Research 16, 678-690.Google Scholar
  15. Schulz, A. and Skutella, M. (1999), The power of α-points in preemptive single machine scheduling. Technical Report Department of Mathematics, Preprint 639/1999. Technical University of Berlin, Berlin.Google Scholar
  16. Seiden, S., Sgall J. and Woeginger, G. (1998), Semi-online scheduling with decreasing job sizes, Operations Research Letters 27(5), 215-221.Google Scholar
  17. Sgall, J. (1999), On-line scheduling - A survey. In: Fiat, A. and Woeginger, G.I. (Eds.), On-line algorithms: The State of the Art, Springer-Verlag, New York.Google Scholar
  18. Smith, W.E. (1956), Various optimizers for single-stage production. Naval Research and Logistics Quarterly 3, 59-66.Google Scholar
  19. Vestjens, A.P.A. (1997), On-line machine scheduling. PhD thesis. Eindhoven University of Technology, The Netherlands.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Jairo R. Montoya-Torres
    • 1
  1. 1.Central CAM and Automation, ST Microelectronics, Z.I. de RoussetRousset CedexFrance (e-mail

Personalised recommendations