The KIPS Transactions:PartA (정보처리학회논문지A)

Korea Information Processing Society (한국정보처리학회)
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Embedding between Hypercube and HCN(n, n), HFN(n, n)

하이퍼큐브와 HCN(n, n), HFN(n, n) 사이의 임베딩

  • Kim, Jong-Seok (Dept.of Computer Science, Graduate School of Sunchon National University) ;
  • Lee, Hyeong-Ok (Dept.of Computer Education, Sunchon National University) ;
  • Heo, Yeong-Nam (Dept.of Computer Science, Sunchon National University)
  • 김종석 (순천대학교 대학원 컴퓨터과학과) ;
  • 이형옥 (순천대학교 컴퓨터교육과) ;
  • 허영남 (순천대학교 컴퓨터과학과)
  • Published : 2002.06.01
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Abstract

It is one of the important measures in the area of algorithm design that any interconnection network should be embedded into another interconnection network for the practical use of algorithm. A HCN(n, n), HFN(n, n) graph also has such a good properties of a hypercube and has a lower network cost than a hypercube. In this paper, we propose a method to embed between hypercube $Q_2n$ and HCN(n, n), HFN(n, n) graph. We show that hypercube $Q_2n$ can be embedded into an HCN(n, n) and KFN(n, n) with dilation 3, and average dilation is smaller than 2. Also, we has a result that the embedding cost, a HCN(n, n) and KFN(n, n) can be embedded into a hypercube, is O(n)

알고리즘의 설계에 있어서 주어진 연결망을 다른 연결망으로 임베딩하는 것은 알고리즘을 활용하는 중요한 방법이다. 상호연결망 HCN(n, n)은 HFN(n, n)은 하이퍼큐브가 갖는 좋은 성질을 가지면서 하이퍼큐브보다 망비용(network cost)이 작은 값을 갖는 상호연결망이다. 본 논문에서는 하이퍼큐브 $Q_{2n}$와 HCN(n, n), HFN(n, n) 사이에 임베딩하는 방법을 제시하고, 하이퍼큐브 $Q_{2n}$은 HCN(n, n)과 HFN(n, n)에 연장율 3, 평균 연장율 2 이하에 임베딩 가능함을 보인다. 또한 HCN(n, n), HFN(n, n)은 하이퍼큐브 $Q_{2n}$에 임베딩하는 비용이 0(n)임을 보인다.

Keywords

References

  1. S. B. Akers and B. Krishnamurthy, 'A Group-Theoretic Model for Symmertric Interconnection Network,' IEEE Trans. Comput., Vol.38, No.4, pp.555-565, 1989 https://doi.org/10.1109/12.21148
  2. K. W. Doty, 'New Designs for Dense processor Interconnection Networks,' IEEE Trans. Computer, Vol.c-33, No.5, May, 1984 https://doi.org/10.1109/TC.1984.1676461
  3. D. R. Duh, G. H. Chen, and J. F. Fang, 'Algorithms and Properties of a New Two-Level Network with Folded Hypercubes as Basic Modules,' IEEE Trans. Parallel Distributed Syst., Vol.6, No.7, pp.714-723, 1995 https://doi.org/10.1109/71.395400
  4. A. El-Amawy and S. Latifi, 'Properties and Performance of Folded Hypercubes,' IEEE Trans. on Parallel Distributed Syst., Vol.2, No.1, pp.31-42, 1991 https://doi.org/10.1109/71.80187
  5. T.-Y. Feng, 'A Survey of Interconnection Networks,' IEEE computer, pp.12-27, December, 1981 https://doi.org/10.1109/C-M.1981.220290
  6. K. Ghose, and K. R. Desai, 'Hierarchical Cubic Networks,' IEEE Trans. Parallel Distributed Syst., Vol.6, No.4, pp.427-436, 1995 https://doi.org/10.1109/71.372797
  7. F. Harary, J. P.,Hayes, and H.-J. Wu, 'A Survey of the Theory of Hipercube Graphs,' Compt. Math. Appl., Vol.15, pp.277-289, 1988 https://doi.org/10.1016/0898-1221(88)90213-1
  8. D. A. Reed and R. M. Fujimoth, Multicomputer Networks : Message-Based Parallel Processing, MIT Press, 1987
  9. A. S. Vaidya, P. S. N. Rao and S. R. Shankar, 'A Class of Hypercube_like Networks,' Proc. of the 5th IEEE Symposium on Parallel and Distributed Processing, pp.800-803, Dec., 1993 https://doi.org/10.1109/SPDP.1993.395450
  10. A. Y. Wu, 'Embedding of Tree Networks into Hypercubes,' J. Parallel and Distributed Computing, Vol.2, pp.238-249, 1985 https://doi.org/10.1016/0743-7315(85)90026-7
  11. S.-K. Yun, and K.-H. Park, 'Comments on 'Hierarchical Cubic Networks',' IEEE Trans. Parallel and Distributed Syst., Vol.9, No.4, pp.410-414, 1998 https://doi.org/10.1109/71.667900
  12. J.P. Hayes and T.N. Mudge, 'Hypercube Supercubes,' Proc. IEEE, Vol.17(12), pp.1829-1841, Dec., 1989 https://doi.org/10.1109/5.48826
  13. L.W. Tucker and G.G. Robertson, 'Architecture and Application of the connection Machine,' IEEE Comput., Vol.21, pp.26-38, Aug., 1988 https://doi.org/10.1109/2.74