Skip to main content
Springer Nature Link
Log in

Scheduling nonlinear divisible loads in a single level tree network

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

In this paper, we study the scheduling problem for polynomial time complexity computational loads in a single level tree network with a collective communication model. The problem of minimizing the processing time is investigated when the computational loads require polynomial order of processing time which is proportional to the size of load fraction. In the divisible load theory framework, the presence of polynomial time complexity computational loads leads to solving higher-order algebraic equations to find the optimal load fractions assigned to the processors in the network. The problem of finding optimal load fraction is a computationally intensive task. Using a mild assumption on the ratio of communication time to computation time, we present a closed-form solution for near optimal load fractions and processing time for the entire load fractions. Finally, we also present a closed-form solution for scheduling polynomial loads with start-up delay in communication and computation. The numerical speedup results obtained using closed-form solution clearly show that super-linear speedup is possible for the polynomial computational loads.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adler M, Gong Y, Rosenberg AL (2003) Optimal sharing of bags of tasks in heterogeneous clusters. In: Proceedings of the annual ACM symposium on parallel algorithms and architectures, San Diego, California, USA, 2003, pp 1–10

    Google Scholar 

  2. Bai Y, Robert RC (2008) Parallel block tridiagonalization of real symmetric matrices. J Parallel Distrib Comput 68:703–715

    Article  MATH  Google Scholar 

  3. Barlas GD (1998) Collection aware optimum sequencing of operations and closed form solutions for the distribution of divisible load on arbitrary processor trees. IEEE Trans Parallel Distrib Syst 9:429–441

    Article  Google Scholar 

  4. Bataineh S, Robertazzi TG (1991) Bus oriented load sharing for a network of sensor driven processors. IEEE Trans Syst Man Cybern 21:1202–1205

    Article  Google Scholar 

  5. Beaumont O, Carter L, Ferrante J, Legrand A, Robert Y (2002) Bandwidth-centric allocation of independent tasks on heterogeneous platforms. In: Proceedings of the international parallel and distributed processing symposium. IEEE Computer Society Press, Los Alamitos

    Google Scholar 

  6. Bharadwaj V, Viswanadham N (2000) Suboptimal solutions using integer approximation techniques for scheduling divisible loads on distributed bus networks. IEEE Trans Syst Man Cybern, Part A, Syst Hum 30:680–691

    Article  Google Scholar 

  7. Bharadwaj V, Ghose D, Mani V (1995) Multi-installment load distribution in tree networks with delay. IEEE Trans Aerosp Electron Syst 31:555–567

    Article  Google Scholar 

  8. Bharadwaj V, Ghose D, Mani V, Robertazzi TG (1996) Scheduling divisible loads in parallel and distributed systems. IEEE Computer Society Press, Los Alamitos

    Google Scholar 

  9. Bharadwaj V, Ghose D, Robertazzi TG (2003) Divisible load theory: a new paradigm for load scheduling in distributed systems. Clust Comput 6:7–18

    Article  Google Scholar 

  10. Blazewicz J, Drozdowski M (1995) Scheduling divisible jobs on hypercubes. Parallel Comput 21:1945–1956

    Article  MathSciNet  Google Scholar 

  11. Blazewicz J, Drozdowski M, Guinand F, Trystram D (1999) Scheduling a divisible task in a 2-dimensional mesh. Discrete Appl Math 94:35–50

    Article  MathSciNet  MATH  Google Scholar 

  12. Cheng YC, Robertazzi TG (1988) Distributed computation with communication delays. IEEE Trans Aerosp Electron Syst 24:700–712

    Article  Google Scholar 

  13. Drozdowski M, Wolniewicz P (2003) Out-of-core divisible load processing. IEEE Trans Parallel Distrib Syst 14:1048–1056

    Article  Google Scholar 

  14. Duda RO, Hart PE (1972) Use of the Hough transformation to detect lines and curves in pictures. Commun ACM 15:11–15

    Article  Google Scholar 

  15. Dutot P-F (2003) Divisible load on heterogeneous linear array. In: Proceedings of the international parallel and distributed processing symposium, Nice, France, 2003

    Google Scholar 

  16. Gropp W, Lusk E, Skjellum A (1994) Using MPI: portable parallel programming with the message-passing interface. MIT Press, Cambridge

    Google Scholar 

  17. Guil N, Villalba J, Zapata EL (1995) A fast Hough transform for segment detection. IEEE Trans Image Process 4(11):1541–1548

    Article  Google Scholar 

  18. Glazek W (2003) A multistage load distribution strategy for three dimensional meshes. Clust Comput 6:31–40

    Article  Google Scholar 

  19. Hung JT, Robertazzi T (2003) Distributed scheduling of nonlinear computational loads. In: Proceedings of the conference on information sciences and systems, March 12–14, 2003, The Johns Hopkins University, Baltimore

    Google Scholar 

  20. Hung JT, Robertazzi TG (2004) Divisible load cut through switching in sequential tree networks. IEEE Trans Aerosp Electron Syst 40:968–982

    Article  Google Scholar 

  21. Hung JT, Robertazzi TG (2004) Scalable scheduling for clusters and grids using cut through switching. Int J Comput Appl 26:147–156

    Google Scholar 

  22. Hung JT, Robertazzi TG (2008) Scheduling nonlinear computational loads. IEEE Trans Aerosp Electron Syst 44(3):1169–1182

    Article  Google Scholar 

  23. Hung JT, Kim HJ, Robertazzi TG (2002) Scalable scheduling in parallel processors. In: Proceedings of the conference on information sciences and systems. Princeton University, Princeton

    Google Scholar 

  24. Khalifa KB, Boubaker M, Chelbi N, Bedoui MH (2008) Learning vector quantization neural network implementation using parallel and serial arithmetic. Int J Comput Sci Eng Syst 2(4):251–256

    Google Scholar 

  25. Kim HJ (2003) A novel load distribution algorithm for divisible loads. Clust Comput 6:41–46

    Article  Google Scholar 

  26. Kim HJ, Jee G-I, Lee JG (1996) Optimal load distribution for tree network processors. IEEE Trans Aerosp Electron Syst 32:607–612

    Article  Google Scholar 

  27. Li K (2003) Parallel processing of divisible loads on partitionable static interconnection networks. Clust Comput 6:47–56

    Article  MATH  Google Scholar 

  28. Othman H, Aboulnasr T (2003) A separable low complexity 2D HMM with application to face recognition. IEEE Trans Pattern Anal Mach Intell 25(10):1229–1238

    Article  Google Scholar 

  29. Piriyakumar DAL, Murthy CSR (1998) Distributed computation for a hypercube network of sensor-driven processors with communication delays including setup time. IEEE Trans Syst Man Cybern, Part A, Syst Hum 28:245–251

    Article  Google Scholar 

  30. Robertazzi TG (1993) Processor equivalence for a linear daisy chain of load sharing processors. IEEE Trans Aerosp Electron Syst 29:1216–1221

    Article  Google Scholar 

  31. Robertazzi TG (2003) Ten reasons to use divisible load theory. Computer 31:63–68

    Article  Google Scholar 

  32. Suresh S, Mani V, Omkar SN, Kim HJ (2006) Divisible load scheduling in distributed system with buffer constraints: Genetic algorithm and linear programming approach. Int J Parallel Emergent Distributed Syst 21(5):303–321

    Article  MathSciNet  MATH  Google Scholar 

  33. Suresh S, Omkar SN, Mani V (2003) The effect of start-up delays in scheduling divisible loads on bus networks: an alternate approach. Comput Math Appl 46(10–11):1545–1557

    Article  MathSciNet  MATH  Google Scholar 

  34. Suresh S, Omkar SN, Mani V (2005) Parallel implementation of back-propagation algorithm in networks of workstations. IEEE Trans Parallel Distrib Syst 16(1):24–34

    Article  Google Scholar 

  35. Yang Y, Casanova H (2003) UMR: a multi-round algorithm for scheduling divisible workloads. In: Proceedings of the international parallel and distributed processing symposium, Nice, France, 2003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University, Singapore, Singapore

    S. Suresh

  2. Division of Information Management and Security, Korea University, Seoul, South Korea

    H. J. Kim & Cui Run

  3. State University of New York, Stony Brook, NY, USA

    T. G. Robertazzi

Authors
  1. S. Suresh
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. H. J. Kim
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Cui Run
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. T. G. Robertazzi
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to S. Suresh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Suresh, S., Kim, H.J., Run, C. et al. Scheduling nonlinear divisible loads in a single level tree network. J Supercomput 61, 1068–1088 (2012). https://doi.org/10.1007/s11227-011-0677-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-011-0677-2

Keywords