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Design and analysis of the rotational binary graph as an alternative to hypercube and Torus

  • Jung-hyun Seo
  • HyeongOk LeeEmail author
Article
  • 9 Downloads

Abstract

Network cost is equal to degree × diameter and is one of the important measurements when evaluating graphs. Torus and hypercube are very well-known graphs. When these graphs expand, a Torus has an advantage in that its degree does not increase. A hypercube has a shorter diameter than that of other graphs, because when the graph expands, the diameter increases by 1. Hypercube Qn has 2n nodes, and its diameter is n. We propose the rotational binary graph (RBG), which has the advantages of both hypercube and Torus. RBGn has 2n nodes and a degree of 4. The diameter of RBGn would be 1.5n + 1. In this paper, we first examine the topology properties of RBG. Second, we construct a binary spanning tree in RBG. Third, we compare other graphs to RBG considering network cost specifically. Fourth, we suggest a broadcast algorithm with a time complexity of 2n − 2. Finally, we prove that RBGn embedded into hypercube Qn results in dilation n, and expansion 1, and congestion 7.

Keywords

Rotational binary graph Graph Interconnection network Torus Hypercube 

Notes

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03032173).

References

  1. 1.
    Mokhtar H, Zhou S (2017) Recursive cubes of rings as models for interconnection networks. Discrete Appl Math 217:639–662MathSciNetCrossRefGoogle Scholar
  2. 2.
    Jahanshahi M, Bistouni F (2018) Interconnection networks. Crossbar-based interconnection networks. Springer, Cham, pp 9–39CrossRefGoogle Scholar
  3. 3.
    McDonald N, Adriana F, Davis A, Isaev M, Kim J, Gibson D (2018) SuperSim: extensible flit-level simulation of large-scale interconnection networks. In: 2018 IEEE International Symposium on Performance Analysis of Systems and Software (ISPASS). IEEE, pp 87–98Google Scholar
  4. 4.
    Mokhtar H (2017) Cube-connected circulants as efficient models for interconnection networks. J Interconnect Netw 17.03n04:1741007CrossRefGoogle Scholar
  5. 5.
    Rahman MMH, Mohammed NMA, Adamu AI, Dhiren KB, Yasuyuki M, Yasushi I (2019) A New static cost-effective parameter for interconnection networks of massively parallel computer systems. In: Soft computing data analytics. Springer, Singapore, pp 147–155Google Scholar
  6. 6.
    Habibian H, Patooghy A (2017) Fault-tolerant routing methodology for hypercube and cube-connected cycles interconnection networks. J Supercomput 73(10):4560–4579CrossRefGoogle Scholar
  7. 7.
    Nai-Wen C, Sun-Yuan H (2018) Conditional diagnosability of (n, k)-star graphs under the PMC model. IEEE Trans Dependable Secure Comput 15(2):207–216CrossRefGoogle Scholar
  8. 8.
    Decayeux C, Seme D (2005) 3D hexagonal network: modeling, topological properties, addressing scheme, and optimal routing algorithm. IEEE Trans Parallel Distrib Syst 16(9):875–884CrossRefGoogle Scholar
  9. 9.
    EI-Amawy A, Latifi S (1991) Properties and performances of folded hypercubes. IEEE Trans Parallel Distrib Syst 2(1):31–42CrossRefGoogle Scholar
  10. 10.
    Efe K (1991) A variation on the hypercube with lower diameter. IEEE Trans Comput 40(11):1312–1316CrossRefGoogle Scholar
  11. 11.
    Mohan KJ, Pataik LM (1992) Extended hypercube: a hierarchical interconnection network of hypercubes. IEEE Trans Parallel Distrib Syst 3(1):45–57CrossRefGoogle Scholar
  12. 12.
    Ghose K, Desai KR (1995) Hierarchical cubic network. IEEE Trans Parallel Distrib Syst 6(4):427–435CrossRefGoogle Scholar
  13. 13.
    Shi W, Srimani PK (2005) Hierarchical star: a new two level interconnection network. J Syst Archit 51:1–14CrossRefGoogle Scholar
  14. 14.
    Yun SK, Park KH (1996) Hierarchical hypercube networks (HHN) for massively parallel computers. J Parallel Distrib Comput 37:194–199CrossRefGoogle Scholar
  15. 15.
    Duh D, Chen G, Fang J (1995) Algorithms and properties of a new two-level network with folded hypercubes as basic modules. IEEE Trans Parallel Distrib Syst 6(7):714–723CrossRefGoogle Scholar
  16. 16.
    Malluhi QM, Bayoumi MA (1994) The hierarchical hypercube: a new interconnection topology for massively parallel system. IEEE Trans Parallel Distrib Syst 5(1):17–30MathSciNetCrossRefGoogle Scholar
  17. 17.
    Seo JH (2013) Three-dimensional Petersen-torus network: a fixed-degree network for massively parallel computers. J Supercomput 64(3):987–1007CrossRefGoogle Scholar
  18. 18.
    Parhami B, Yeh CH (2000) Why network diameter is still important. In: Proceedings of International Conference on Communications in Computing, pp 271–274Google Scholar
  19. 19.
    Saad Y, Schultz MH (1988) Topological properties of hypercubes. IEEE Trans Comput 37(7):867–872CrossRefGoogle Scholar
  20. 20.
    Seo Jung-Hyun et al (2018) The hierarchical Petersen network: a new interconnection network with fixed degree. J Supercomput 74(4):1636–1654CrossRefGoogle Scholar
  21. 21.
    Seo JH, Lee H (2013) Link-disjoint broadcasting algorithm in wormhole-routed 3D Petersen–Torus networks. Int J Distrib Sens Netw 9(12):501974CrossRefGoogle Scholar
  22. 22.
    Seo JH, Lee H (2016) Embedding algorithm among half pancake, pancake, and star graphs. Int J Softw Eng Appl 10(3):191–204Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.Department of Multimedia EngineeringNational University of ChonnamYeosuRepublic of Korea
  2. 2.Department of Computer EducationNational University of SunchonSunchonRepublic of Korea

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