Skip to main content
Log in

Better traffic distribution one-to-all broadcast in higher dimensional Gaussian networks

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

Abstract

A higher dimensional Gaussian network, \(G_\alpha ^n\), has been proposed in Shamaei et al. (IEEE 28th international parallel and distributed processing symposium workshops, pp 1438–1447, 2014) as a useful alternative of the classical multi-dimensional torus network. The one-to-all broadcast is a well-known algorithm that spreads a message from one node to all other nodes in the network. This paper presents an improved one-to-all broadcasting algorithm in \(G_\alpha ^n\) that achieves a lower average number of steps to receiving the broadcasted message. Furthermore, the all-to-all broadcasting method is illustrated based on dividing the proposed one-to-all broadcasting algorithm into four phases. The analytical and simulation results show that the proposed algorithm achieves better traffic performance than the current known algorithm and has 4.1 % less total number of senders.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Albader B, Bose B, Flahive M (2012) Efficient communication algorithms in hexagonal mesh interconnection networks. IEEE Trans Parallel Distrib Syst 23(1):69–77

    Article  Google Scholar 

  2. Arabnia H, Bhandarkar S (1996) Parallel stereocorrelation on a reconfigurable multi-ring network. J Supercomput 10(3):243–269

    Article  MATH  Google Scholar 

  3. Arabnia H, Oliver M (1987) Arbitrary rotation of raster images with simd machine architectures. Comput Graph Forum 6(1):3–11

    Article  Google Scholar 

  4. Arabnia H, Oliver M (1989) A transputer network for fast operations on digitised images. Comput Graph Forum 8(1):3–11

    Article  Google Scholar 

  5. Arabnia HR (1990) A parallel algorithm for the arbitrary rotation of digitized images using process-and-data-decomposition approach. J Parallel Distrib Comput 10(2):188–192

    Article  Google Scholar 

  6. Arabnia HR (1996) Distributed stereo-correlation algorithm. Comput Commun 19(8):707–711

    Article  Google Scholar 

  7. Arabnia HR, Oliver MA (1987) A transputer network for the arbitrary rotation of digitised images. Comput J 30(5):425–433

    Article  Google Scholar 

  8. Arabnia HR, Smith JW (1993) A reconfigurable interconnection network for imaging operations and its implementation using a multi-stage switching box. In: Proceedings of the 7th annual international high performance computing conference, pp 349–357

  9. Bhandarkar S, Arabnia H (1995) The hough transform on a reconfigurable multi-ring network. J Parallel Distrib Comput 24(1):107–114

    Article  Google Scholar 

  10. Bhandarkar SM, Arabnia HR (1995) The REFINE multiprocessor theoretical properties and algorithms. Parallel Comput 21(11):1783–1805

    Article  Google Scholar 

  11. Bhandarkar SM, Arabnia HR, Smith JW (1995) A reconfigurable architecture for image processing and computer vision. Int J Pattern Recognit Artif Intell 09(02):201–229

    Article  Google Scholar 

  12. Bhuyan L, Agrawal D (1984) Generalized hypercube and hyperbus structures for a computer network. IEEE Trans Comput C–33(4):323–333

    Article  Google Scholar 

  13. Deo N (1974) Graph theory with applications to engineering and computer science (prentice hall series in automatic computation). Prentice-Hall Inc., Upper Saddle River

    Google Scholar 

  14. Duato J, Yalamanchili S, Ni L (1997) Interconnection networks: an engineering approach, 1st edn. IEEE Computer Society Press, Los Alamitos

    Google Scholar 

  15. Flahive M, Bose B (2010) The topology of Gaussian and Eisenstein–Jacobi interconnection networks. IEEE Trans Parallel Distrib Syst 21(8):1132–1142

    Article  Google Scholar 

  16. Grama A, Gupta A, Karypis G, Kumar V (2003) Introduction to parallel computing, 2nd edn. Addison-Wesley Longman Publishing Co., Inc., Boston

    Google Scholar 

  17. Hardy GH, Wright EM (1980) An introduction to the theory of numbers (Oxford science publications), 5th edn. Oxford University Press, USA

    Google Scholar 

  18. Huber K (1994) Codes over Gaussian integers. IEEE Trans Inf Theory 40(1):207–216

    Article  MATH  Google Scholar 

  19. Jordan JH, Potratz CJ (1965) Complete residue systems in the Gaussian integers. Math Mag 38(1):1–12

    Article  MATH  MathSciNet  Google Scholar 

  20. Martinez C, Beivide R, Stafford E, Moreto M, Gabidulin E (2008) Modeling toroidal networks with the Gaussian integers. IEEE Trans Comput 57(8):1046–1056

    Article  MathSciNet  Google Scholar 

  21. Martinez C, Vallejo E, Beivide R, Izu C, Moreto M (2006) Dense Gaussian networks: suitable topologies for on-chip multiprocessors. Int J Parallel Program 34:193–211

    Article  MATH  Google Scholar 

  22. Shamaei A, Bose B, Flahive M (2014) Higher dimensional Gaussian networks. In: IEEE 28th international parallel and distributed processing symposium workshops, pp 1438–1447

  23. Wani M, Arabnia H (2003) Parallel edge-region-based segmentation algorithm targeted at reconfigurable multiring network. J Supercomput 25(1):43–62

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zaid Hussain.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hussain, Z. Better traffic distribution one-to-all broadcast in higher dimensional Gaussian networks. J Supercomput 71, 4381–4399 (2015). https://doi.org/10.1007/s11227-015-1532-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-015-1532-7

Keywords

Navigation