Dynamic Windows Scheduling with Reallocation 

  • Martín Farach-Colton
  • Katia Leal
  • Miguel A. Mosteiro
  • Christopher Thraves
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8504)

Abstract

We consider the Windows Scheduling problem. The problem is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, the problem is to schedule the use of communication channels that allow at most one transmission per time slot, to clients specified by a maximum delay between consecutive transmissions. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We present three online reallocation algorithms for Windows Scheduling. We analyze one of them and we evaluate experimentally all three showing that, in practice, they achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting trade-offs between reallocations and channel usage. To the best of our knowledge, this is the first study of Windows Scheduling with reallocation costs.

Keywords

Reallocation Algorithms Windows Scheduling Radio Networks Unit Fractions Bin Packing 

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References

  1. 1.
    Balogh, J., Békési, J.: Semi-on-line bin packing: A short overview and a new lower bound. Central European Journal of Operations Research, 1–14 (2012)Google Scholar
  2. 2.
    Balogh, J., Békési, J., Galambos, G., Reinelt, G.: On-line bin packing with restricted repacking. Journal of Combinatorial Optimization, 1–17 (2012)Google Scholar
  3. 3.
    Bar-Noy, A., Bhatia, R., Naor, J., Schieber, B.: Minimizing service and operation costs of periodic scheduling. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 11–20 (1998)Google Scholar
  4. 4.
    Bar-Noy, A., Ladner, R.E.: Windows scheduling problems for broadcast systems. SIAM Journal on Computing 32(4), 1091–1113 (2003)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Bar-Noy, A., Ladner, R.E., Tamir, T.: Windows scheduling as a restricted version of bin packing. ACM Transactions on Algorithms (TALG) 3(3), 28 (2007)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Bender, M.A., Farach-Colton, M., Fekete, S.P., Fineman, J.T., Gilbert, S.: Reallocation problems in scheduling. In: 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2013, pp. 271–279 (2013)Google Scholar
  7. 7.
    Chan, J.W.-T., Lam, T.-W., Wong, P.W.H.: Dynamic bin packing of unit fractions items. Theoretical Computer Science 409(3), 521–529 (2008)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Chan, W.-T., Wong, P.W.H.: On-line windows scheduling of temporary items. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 259–270. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    M. Farach-Colton, K. Leal, M.A. Mosteiro, C. Thraves. Dynamic windows scheduling with reallocation. arXiv:1404.1087 (April 2014)Google Scholar
  10. 10.
    Han, X., Peng, C., Ye, D., Zhang, D., Lan, Y.: Dynamic bin packing with unit fraction items revisited. Information Processing Letters 110(23), 1049–1054 (2010)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Heydari, M., Sadjadi, S.J., Mohammadi, E.: Minimizing total flow time subject to preemption penalties in online scheduling. The International Journal of Advanced Manufacturing Technology 47(1-4), 227–236 (2010)CrossRefGoogle Scholar
  12. 12.
    Ivkovic, Z., Lloyd, E.L.: Fully dynamic algorithms for bin packing: Being (mostly) myopic helps. SIAM Journal on Computing 28(2), 574–611 (1998)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Liu, Z., Edwin Cheng, T.C.: Minimizing total completion time subject to job release dates and preemption penalties. Journal of Scheduling 7(4), 313–327 (2004)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Sanders, P., Sivadasan, N., Skutella, M.: Online scheduling with bounded migration. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1111–1122. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Shachnai, H., Tamir, T., Woeginger, G.J.: Minimizing makespan and preemption costs on a system of uniform machines. Algorithmica 42(3-4), 309–334 (2005)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
  17. 17.
    WestBrook, J.: Load balancing for response time. Journal of Algorithms 35(1), 1–16 (2000)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Yu, H., Xu, Y., Wu, T.: Online inventory replenishment scheduling of temporary orders. Information Processing Letters 113(5), 188–192 (2013)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Martín Farach-Colton
    • 1
    • 2
  • Katia Leal
    • 3
  • Miguel A. Mosteiro
    • 4
  • Christopher Thraves
    • 3
  1. 1.Dept. of Computer ScienceRutgers UniversityPiscatawayUSA
  2. 2.Tokutek Inc.USA
  3. 3.GSyC, Universidad Rey Juan CarlosMadridSpain
  4. 4.Dept. of Computer ScienceKean UniversityUnionUSA

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