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

한국정보과학회 (Korean Institute of Information Scientists and Engineers)
권호 표지

폴디드 하이퍼큐브와 이븐연결망, 오드연결망 사이의 임베딩 알고리즘

Embedding Algorithm among Folded Hypercube, Even Network and Odd Network

  • 김종석 (영남대학교 전자공학부) ;
  • 심현 (순천대학교 컴퓨터공학과) ;
  • 이형옥 (순천대학교 컴퓨터교육과)
  • 발행 : 2008.08.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 하이퍼큐브보다 망비용이 개선된 폴디드 하이퍼큐브 연결망과 이븐연결망, 오드 연결망 사이의 임베딩을 분석한다. 연구 결과로 폴디드 하이퍼큐브 $FQ_n$을 이븐연결망 $E_{n-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보이고, 이븐연결망 $E_d$을 폴디드 하이퍼큐브 $FQ_{2d-3}$에 연장율 1에 임베딩 가능함을 보인다. 또한, 폴디드 하이퍼큐브 $FQ_n$는 오드연결망 $O_{n-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보이고, 오드연결망 $O_d$는 폴디드 하이퍼큐브 $FQ_{2d-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보인다. 마지막으로, 이븐연결망 $E_d$는 오드연결망 $O_d$에 연장을 2, 밀집을 1에 임베딩 가능함을 보이고, 오드연결망 $O_d$는 이븐연결망 $E_{d-1}$에 연장율 2, 밀집율 1에 임베딩 가능함을 보인다.

In this paper, we will analyze embedding among Folded Hypercube, Even Network and Odd Network to further improve the network cost of Hypercube. We will show Folded Hypercube $FQ_n$ can be embedded into Even Network $E_{n-1}$ with dilation 2, congestion 1 and Even Network $E_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 1. Also, we will prove Folded Hypercube $FQ_n$ can be embedded into Odd Network $O_{n-1}$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $FQ_{2d-3}$ with dilation 2, congestion 1. Finally, we will show Even Network $E_d$ can be embedded into Odd Network $O_d$ with dilation 2, congestion 1 and Odd Network $O_d$ can be embedded into Folded Hypercube $E_{d-1}$ with dilation 2, congestion 1.

키워드

참고문헌

  1. A. El-Amawy and S. Latifi, "Properties and Performance of Folded Hypercubes," IEEE Trans. Parallel Distributed syst., Vol.2, No.1, pp.31-42, 1991 https://doi.org/10.1109/71.80187
  2. A. Ghafoor, "A Class of Fault-Tolerant Multiprocessor Networks," IEEE Trans. Reliability, Vol.38, No.1, pp.5-15, 1989 https://doi.org/10.1109/24.24569
  3. A. Ghafoor and T. R. Bashkow, "A Study of Odd Graphs as Fault-Tolerant Interconnection Networks," IEEE Trans. Computers, Vol.40, No.2 pp.225-232, 1991 https://doi.org/10.1109/12.73594
  4. S. Bettayeb, B. Cong, M. Girou and I.H. Sudborough, "Embedding Star Networks into Hypercubes," IEEE Trans. Computers, Vol.45, No.2 pp.186-194, 1996
  5. J. Fan, X. Jia, and X. Lin, "Optimal Embedding of Paths with Varios Lengths in Twisted Cubes," IEEE Trans. Parallel Distributed syst., Vol.18, No.4, pp.511-521, 2007 https://doi.org/10.1109/TPDS.2007.1003
  6. M. Hamdi and S. W. Song, "Embedding Hierarchical Hypercube Networks into the Hypercube," IEEE Trans. Parallel Distributed syst., Vol.8, No.9, pp.897-902, 1997 https://doi.org/10.1109/71.615435
  7. J.-C. Lin, T.-H. Chi, H.-C. Keh, and A.-H. A. Lion, "Embedding of Complete Binary Tree with 2-Expansion in a Faulty Flexible Hypercube," Journal of Systems Architecture, Vol.47, No.6, pp.543-548, 2001 https://doi.org/10.1016/S1383-7621(01)00004-2
  8. X. Shen, W. Liang, and Q. Hu, "On Embedding between 2D Meshes of the Same Size," IEEE Trans. Computers, Vol.46, No.8, pp.880-889, 1997 https://doi.org/10.1109/12.609277
  9. C. N. Lai, G. H. Chen and D. R. Duh, "Constructing One-to-Many Disjoint Paths in Folded Hypercubes," IEEE Trans. Computers, Vol.51, No.1 pp.33-45, 2002 https://doi.org/10.1109/12.980015
  10. J.-M. Xu and M. Ma, "Cycles in Folded Hypercubes," Appl. Math. Lett., Vol.19, pp.140-145, 2006 https://doi.org/10.1016/j.aml.2005.04.002
  11. N. Biggs, "Some Odd Graph Theory," Annals of New York Academy of Sciences, Vol. 319, pp.71- 81, 1979 https://doi.org/10.1111/j.1749-6632.1979.tb32775.x