The Journal of Supercomputing

, Volume 59, Issue 2, pp 569–588 | Cite as

Comparative analysis of Traffic Patterns on k-ary n-tree using adaptive algorithms based on Burton Normal Form



k-ary n-trees are a particular type of Fat-Trees that belong to parametric family of topologies. In spite of their wide usage as an Interconnection Network topology, it has been quite unclear about the performance of Adaptive Routing Algorithms on them. In this paper, we consider a 4-ary 3-tree and analyze two Adaptive Routing Algorithms namely the Non-Minimal Adaptive Routing Algorithm and Minimal Adaptive Routing Algorithm. Specifically, the application of these algorithms on 4-ary 3-tree using various Traffic Patterns has been simulated. The six Traffic Patterns called BitTranspose, BitReversal, BitComplement, Uniform Distribution, k-shift and Ring are used as running examples throughout the paper. The simulation results show that the Network Latency for k-ary n-tree is much higher in case of the Non-Minimal Algorithm as compared to the Minimal Algorithm. However, in case of Ring Traffic, the results show a deviant behavior when compared to other patterns.


Index Terms Interconnection networks Fat-trees k-ary n-trees Traffic Patterns Non-Minimal Adaptive Routing Minimal Adaptive Routing BigNetSim Burton Normal Form Congestion-free patterns and flow-control 


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  1. 1.
    Nitin, Subramanian A (2008) Efficient algorithms to solve dynamic MINs stability problems using stable matching with complete TIES. J Discrete Algorithms 6(3):353–380 CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Nitin, Garhwal S, Srivastava N (2009) Designing a fault-tolerant fully-chained combining switches multi-stage interconnection network with disjoint paths. J Supercomput. doi: 10.1007/s11227-009-0336-z
  3. 3.
    Nitin, Chauhan DS, Sehgal VK (2008) Two O(n 2) time fault-tolerant parallel algorithm for inter NoC communication in NiP. Springer, Berlin, ISBN: 978-3-540-79186-7, pp 267–282. Invited Google Scholar
  4. 4.
    Nitin, Vaish R, Shrivastava U, Rana M (2009) Adaptive deterministic routing algorithm for k-ary n-cube torus network. In: 7th Annual workshop on Charm++ and its applications. Parallel Programming Lab, University of Illinois, Urbana Champaign Google Scholar
  5. 5.
    Nitin, Sehgal VK, Bansal PK (2007) On MTTF analysis of a fault-tolerant hybrid MINs. WSEAS Trans Comput Res 2(2):130–138 Google Scholar
  6. 6.
    Nitin (2006) Component level reliability analysis of fault-tolerant hybrid MINs. WSEAS Trans Comput 5(9):1851–1859 Google Scholar
  7. 7.
    Dally WJ, Towels B (2005) Principles and practices of interconnection networks. Morgan Kaufmann, San Mateo Google Scholar
  8. 8.
    Wani MA, Arabnia HR (2003) Parallel edge-region-based segmentation algorithm targeted at reconfigurable multi-ring network. J Supercomput 25(1):43–63 CrossRefMATHGoogle Scholar
  9. 9.
    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):188–193 CrossRefGoogle Scholar
  10. 10.
    Arabnia HR, Oliver MA (1989) A transputer network for fast operations on digitised images. Int J Eurograph Assoc 8(1):3–12 Google Scholar
  11. 11.
    Singh A, Dally WJ, Gupta AK, Towles B (2004) Adaptive channel queue routing on k-ary n-cubes. In: Proceedings of the 16th annual ACM symposium on parallelism in algorithms and architectures, pp 11–19 Google Scholar
  12. 12.
    Dally WJ (1990) Network and processor architecture for message-driven computers, VLSI and parallel computers. Morgan Kaufmann, San Mateo, pp 140–222 Google Scholar
  13. 13.
    Gomez C, Gilabert F, Gomez ME, Lopez P, Duato J (2007) Deterministic versus adaptive routing in fat-trees. In: Proceedings of the international parallel and distributed processing symposium, p 297 Google Scholar
  14. 14.
    Leighton FT (1992) Introduction to parallel algorithms and architectures: arrays, trees, hypercubes. Morgan Kaufmann, San Mateo MATHGoogle Scholar
  15. 15.
    Petrini F, Vanneschi M (1997) k-ary n-trees: high performance networks for massively parallel architecture. In: Proceedings of the 11th international parallel processing symposium, pp 87–93 Google Scholar
  16. 16.
    Gomez C, Gilabert F, Gomez ME, Lopez P, Duato J (2007) An efficient fault-tolerant routing methodology for fat tree interconnection networks. In: Proceedings of the 5th international symposium on parallel and distributed processing and applications, pp 509–522 Google Scholar
  17. 17.
    Nguyen TD, Synder L (1994) Performance analysis of a minimal adaptive router. In: Lecture notes in computer science, vol 853. Springer, Berlin, pp 31–44 Google Scholar
  18. 18.
    Bolding K, Fulgham M, Synder L (1997) The case for chaotic adaptive routing. IEEE Trans Comput 46(12):1281–1292 CrossRefGoogle Scholar
  19. 19.
    Zheng G, Kakulapati G, Kale LV (2004) BigSim: a parallel simulator for performance prediction of extremely large parallel machines. In: Proceedings of the 18th international parallel and distributed processing symposium, vol 1, p 78b Google Scholar
  20. 20.
    Wilmarth TL, Zheng G, Bohm EJ, Mehta Y, Choudhury N, Jagadishprasad P, Kale LV (2005) Performance prediction using simulation of large-scale interconnection networks in POSE. In: Proceedings of the 19th workshop on principles of advanced and distributed simulation, pp 109–118 Google Scholar
  21. 21.
    Kale LV, Krishnan S (1993) CHARM++: a portable concurrent object oriented system based on C++. ACM SIGPLAN Notices 28(10):91–108 CrossRefGoogle Scholar
  22. 22.
    Choudhury N, Mehta T.L. Wilmarth Y, Bohm EJ, Kale LV (2005) Scaling an optimistic parallel simulation of large scale interconnection networks. In: Proceedings of the 37th conference on winter simulation, pp 591–600 Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of CSE and ITJaypee University of Information TechnologySolanIndia
  2. 2.Uttarakhand Technical UniversityDehradunIndia

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