Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Hyper-Torus : A New Torus Network based on 3-dimensional Hypercube

하이퍼-토러스 : 3차원 하이퍼큐브 기반의 새로운 토러스 네트워크

  • 기우서 (순천대학교 컴퓨터과학과) ;
  • 김정섭 (한국교원대학교 수학교육과) ;
  • 이형옥 (순천대학교 컴퓨터교육과) ;
  • 오재철 (순천대학교 컴퓨터과학과)
  • Published : 2009.06.15
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Abstract

In this paper, we propose the new torus network which has the hypercube Q3 as the basic module. The proposed Hyper-torus has the degree 4, and is the network which has the scalability, and the fine diameter. If we compare the class of the torus in the viewpoint of network cost, the hyper-torus with $1.4{\sqrt{N}}$+ 16 is proved to be approximately 65% than the torus with $4{\sqrt{N}}$ and 50% than the honeycomb with $2.45{\sqrt{N}}$. This result means that hyper-torus is better for the class of the existing mesh in the viewpoint of network cost.

본 논문에서는 3차원 하이퍼큐브 Q3를 기본모듈로 갖는 새로운 토러스 네트워크를 제안한다. 제안한 하이퍼-토러스는 분지수 4를 갖고, 확장성, 지름이 좋은 연결망이다. 토러스 부류를 망비용 관점에서 비교하면 하이퍼-토러스는 $1.4{\sqrt{N}}$+16으로 토러스의 망비응 $4{\sqrt{N}}$보다 대략 65% 개선되었고, 허니컴 토러스의 망비용$ 2.45{\sqrt{N}}$보다 대략 50% 개선된 값이다. 이러한 결과는 하이퍼-토러스가 기존의 메시 부류보다 망비용 관점에서 우수함을 의미한다.

Keywords

References

  1. S. Abraham and K. Padmanabhan, "An Analysis of the Twisted Cube Topology," Proc. of the Int. Conference Parallel Processing, pp. 116-120, Aug. 1989.
  2. S. B. Akers, D. Harel and B. Krishnamurthy, "The Star Graph: An Attractive Alternative to the n-Cube," Proc. of the Int. Conference Parallel Processing, pp. 393-400, 1987.
  3. K. Efe, "A Variation on the hypercube with Lower Diameter," IEEE trans. computer, Vol.40, No.11, pp. 1312-1316, 1991. https://doi.org/10.1109/12.102840
  4. B. Parhami and M. Rakov, "Perfect Difference Networks and Related Interconnection Structures for Parallel and Distributed Systems," IEEE trans. on Parallel and Distributed Systems, Vol.16, No.8, pp. 714-724, Aug. 2005. https://doi.org/10.1109/TPDS.2005.96
  5. C. D. Thompson and H. T. Kung, "Sorting on a Mesh-Connected Parallel Computer," Communications of the ACM, Vol.20 No.4, pp. 263-271, April 1977. https://doi.org/10.1145/359461.359481
  6. K. W. Tang and S. A. Padubidri, "Diagonal and toroidal Mesh Networks," IEEE trans. computer, Vol.43, No.7 pp. 815-826, Jul 1994. https://doi.org/10.1109/12.293260
  7. M. S. Chen and K. G. Shin, "Addressing, Routing, and Broadcasting in Hexagonal Mesh Multiprocessors," IEEE trans. comput., Vol.39, No.1 pp. 10-18, Jan 1990. https://doi.org/10.1109/12.46277
  8. I. Stojmenovic, "Honeycomb Network: Topological Properties and Communication Algorithms," IEEE trans. on Parallel and Distributed Systems, Vol.8, No.10, pp. 1036-1042, Oct 1997. https://doi.org/10.1109/71.629486
  9. 서정현, 이형옥, 장문석, "멀티컴퓨팅 시스템을 위한 피터슨-토러스(PT) 네트워크", 정보과학회논문지 제35권 6호, pp. 263-272, 2008.
  10. Y. Saad and M. H. Schultz, "Topological Properties of hypercubes," IEEE trans. Computer., Vol.37, No.7, pp. 867-872, July 1988. https://doi.org/10.1109/12.2234
  11. A. EI-Amawy and S. Latifi, "Properties and Performances of Folded hypercubes," IEEE trans. Parallel and Distributed System, Vol.2, No.1, pp. 31-42, 1991. https://doi.org/10.1109/71.80187
  12. 주낙근, 임형석, "그래프 연산과 그레이 코드를 이용한 상호연결망의 설계", 정보과학회논문지, 제19권 1호, pp. 587-590, 1992.
  13. C-H Yeh and E. Varvarigos, "Macro-Star Networks: Efficient Low-Degree Alternatives to Star Graphs for Large-Scale Parallel Architectures," Frontier'96, Symp. on the Frontiers of Massively Parallel Computation, Oct. 1996.
  14. S. Latifi and P. K. Srimani, "Transposition Networks as a Class of Fault-Tolerant Robust Networks," IEEE trans. Comput., Vol.45, No.2, pp. 230-238, Feb. 1996. https://doi.org/10.1109/12.485375
  15. Akl S. G. and Stojmenovic I., "Fundamental algorithm for the star and pancake interconnection networks with applications to computational geometry," Networks, Vol.23, pp. 215-225, 1993. https://doi.org/10.1002/net.3230230403
  16. Q. M. Malluhi and M. A. Bayoumi, "The Hierarchical hypercube: A New Interconnection Topology for Massively Parallel Systems," IEEE trans. Parallel and Distributed System, Vol.5, No.1, pp. 17-30, Jan. 1994. https://doi.org/10.1109/71.262585
  17. D.-R. Duh, G.-H Chen and J.-F. Fang, "Algorithm and Properties of a New Two-level Network with Folded hypercubes as Basic Modules," IEEE trans. Parallel and Distributed System, Vol.6, No.7, pp. 714-723, 1995. https://doi.org/10.1109/71.395400
  18. W. Shi and P. K. Srimani, "Hierarchical star: a new two level interconnection network," Journal of Systems Architecture, Vol.51, No.2, pp. 1-14, 2005. https://doi.org/10.1016/j.sysarc.2004.05.003
  19. Ohring and S. K. DAS, "Folded Petersen cube networks: new competitors for the hypercubes," IEEE trans. on Parallel and Distributed Systems, Vol.7, No.2, pp. 151-168, Feb 1996. https://doi.org/10.1109/71.485505
  20. L. Wang, ZP. Chen and XH Jiang, "Ringed Petersen Spheres Connected hypercube Interconnection Networks," Proceedings of the 10th IEEE International Conference on Engineering of Complex Computer Systems (ICECCS'05), pp. 127-131, 2005.
  21. S.-C. Ku, B.-F. Wang and T-K. Hung, "Constructing Edge-Disjoint Spanning Trees in Product Networks," IEEE Trans. Parallel and Distributed System, Vol.14, No.3, pp. 213-221, 2003. https://doi.org/10.1109/TPDS.2003.1189580
  22. C. Decayeux and D. Seme, "3D hexagonal Network: Modeling, Topological properties, Addressing Scheme, and Optimal Routing Algorithm," IEEE trans. Parallel and Distributed System, Vol.16, No.9, pp. 875-884, 2005. https://doi.org/10.1109/TPDS.2005.100
  23. A. Gonzalez, V. Garcia and L. D. Cerio, "Executing Algorithm with Hypercube Topology on Torus Multicomputers," IEEE trans. on Parallel and Distributed Systems, Vol.6, No.8, pp. 803-814, Feb 1995. https://doi.org/10.1109/71.406957