Harmonic Block Windows Scheduling Through Harmonic Windows Scheduling

  • Yi Sun
  • Tsunehiko Kameda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3665)


In Harmonic windows scheduling (HWS), a data file is divided into N pages and the pages are scheduled in c channels in such a way that each page i appears at least once in some channel in every window of size i. The optimal HWS problem aims to maximize N. Let κ be the largest integer satisfying H κ c, where H n is the n th harmonic number. Then κ is an upper bound on N, if the HWS framework is used. Thus an optimal HWS schedule wastes “bandwidth” at least cH κ . Harmonic block windows scheduling (HBWS) generalizes HWS by grouping b consecutive pages into a superpage. Let N be the total number of pages scheduled. The ratio N/b is directly proportional to the maximum initial waiting time in Media-on-Demand applications. We propose a method that starts with a HWS schedule and modifies it to generate a HBWS schedule that achieves a higher ratio N/b. For up to five channels, we demonstrate that we can always achieve N/b >κ. We also prove that as we increase b, N/b approaches the theoretical upper bound.


Block Size Base Tree Round Robin Feasible Schedule Cyclic Schedule 
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  1. 1.
    Bar-Noy, A., Ladner, R.E.: Windows scheduling problems for broadcast systems. In: Proc. 13th ACM-SIAM Symp. on Discrete Algorithms, pp. 433–442 (2002)Google Scholar
  2. 2.
    Bar-Noy, A., Nisgav, A., Patt-Shamir, B.: Nearly optimal perfectly-periodic schedules. In: Proc. 20th ACM Symp. on Principle of Distributed Computing, pp. 107–116 (2001)Google Scholar
  3. 3.
    Bar-Noy, A., Bhatia, R., Naor, J., Schieber, B.: Minimizing service and operation costs of periodic scheduling. Mathematics of Operations Research 27, 518–544 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bar-Noy, A., Gosh, J., Ladner, R.E.: Off-line and on-line guaranteed start-up delay for media-on-demand with stream merging. In: Proc. 15th ACM Symp. Parallel Algorithms and Atchitectures, pp. 164–173 (2003)Google Scholar
  5. 5.
    Bar-Noy, A., Ladner, R.E., Tamir, T.: Scheduling techniques for media-on-demand. In: Proc. ACM-SIAM Symp. on Discrete Algorithms, pp. 791–800 (2003)Google Scholar
  6. 6.
    Engebretsen, L., Sudan, M.: Harmonic broadcasting is optimal. In: Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (2002)Google Scholar
  7. 7.
    Hua, K.A., Cai, Y., Sheu, S.: Patching: a multicast technique for true video-on-demand services. In: Proc. ACM Multimedia, pp. 191–200 (1998)Google Scholar
  8. 8.
    Hu, A., Nikolaidis, I., Van Beek, P.: On the design of efficient video-on-demand broadcast schedules. In: Proc. 7th Int’l. Symp. on Modeling, Analysis and Simulation of Computer and Telecommunication Systems, pp. 262–269 (1999)Google Scholar
  9. 9.
    Juhn, L., Tseng, L.: Harmonic broadcasting protocols for video-ondemand service. IEEE Trans. on Broadcasting 43, 268–271 (1997)CrossRefGoogle Scholar
  10. 10.
    Lin, Z.: Near-Optimal Heuristic Solutions to Truncated Harmonic Windows Scheduling and Harmonic Group Windows Scheduling. M.Sc. Thesis. School of Computing Science. Simon Fraser University (2004)Google Scholar
  11. 11.
    Ma, F.: Comparison of broadcasting schemes and stream-merging schemes for video-on-demand. CMPT415 Course Project Report (2003)Google Scholar
  12. 12.
    Pâris, J.-F.: A simple low-bandwidth broadcasting protocol for video-ondemand. In: Proc. 8th Int’l. Conf. on Computer Communications and Networks, pp. 118–123 (1999)Google Scholar
  13. 13.
    Pâris, J.-F., Carter, S.W., Long, D.D.E.: A low-bandwidth broadcasting protocol for video-on-demand. In: Proc. 7th Int’l. Conf. on Computer Communications and Networks, pp. 690–697 (1998)Google Scholar
  14. 14.
    Sun, Y., Kameda, T.: Harmonic block windows scheduling for video-on-demand. School of Computing Science, Simon Fraser University. Tech. Rept. 2005-05 (2005), (Submitted for publication)
  15. 15.
    Tseng, Y.-C., Yang, M.-H., Chang, C.-H.: A recursive frequency-splitting scheme for broadcasting hot videos in VOD service. IEEE Trans. on Communications 50, 1348–1355 (2002)CrossRefGoogle Scholar
  16. 16.
    Van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. Kluwer Academic Publishers, Dordrecht (1987)zbMATHGoogle Scholar
  17. 17.
    Yan, E.M., Kameda, T.: An efficient VOD broadcasting scheme with user bandwidth limit. In: Proc. SPIE/ACM Conf. on Multimedia Computing and Networking, vol. 5019, pp. 200–208 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yi Sun
    • 1
  • Tsunehiko Kameda
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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