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

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

Constructing Algorithm for Optimal Edge-Disjoint Spanning Trees in Odd Interconnection Network $O_d$

오드 연결망 $O_d$에서 에지 중복 없는 최적 스패닝 트리를 구성하는 알고리즘

  • 김종석 (영남대학교 정보통신공학과) ;
  • 이형옥 (순천대학교 컴퓨터교육과) ;
  • 김성원 (영남대학교 정보통신공학과)
  • Published : 2009.10.15
Download PDF
⟨ Previous Next ⟩

Abstract

Odd network was introduced as one model of graph theory. In [1], it was introduced as a class of fault-tolerant multiprocessor networks and analyzed so many useful properties such as simple routing algorithms, maximal fault tolerance, node axsjoint path, etc. In this paper, we sauw a construction algorithm of edge-axsjoint spanning trees in Odd network $O_d$. Also, we prove that edge-disjoint spanning tree generated by our algorithm is optimal edge-disjoint spanning tree.

오드 연결망은 그래프이론 모델의 하나로 발표되었는데, [1]에서 고장허용 다중컴퓨터에 대한 하나의 모형으로 소개되었고, 여러 가지 유용한 성질들 - 간단한 라우팅 알고리즘, 최대고장허용도, 노드 중복 없는 경로 등 - 이 분석되었다 본 논문에서는 오드 연결망 $O_d$ 에서 에지 중복 없는 스패닝 트리를 구성하는 알고리즘을 제안한다. 그리고 제안한 알고리즘에 의해 구성된 에지 중복 없는 스패닝 트리가 에지 중복 없는 최적 스패닝 트리임을 증명한다.

Keywords

References

  1. 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
  2. S. B. Akers, D. Harel, and B. Krishnamurthy, "The Star Graph: An Attractive Altermative to the n-Cube," Proc. Int'l. Conf. on Parallel Processing, pp.393-400, 1987.
  3. 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
  4. J.-S. Kim, E. Chen, L. Liptak and H.-O. Lee, "Embedding hypercubes, rings and odd graphs into Hyper-stars," International Journal of Computer Mathematics, vol.86, no.5, pp.771-778, 2009. https://doi.org/10.1080/00207160701691431
  5. J.-S. Kim, H.-O. Lee, "Comments on " A Study of Odd Graphs as Fault-Tolerant Interconnection Networks," IEEE Transaction on Computers, vol.57, no.6, p.864, 2008. https://doi.org/10.1109/TC.2008.53
  6. J.-S. Kim, H.-O. Lee, "One-to-All Broadcasting of Odd Networks for One-port and All-port Models," ETRI Journal, vol.30, no.6, pp.856-858, 2008. https://doi.org/10.4218/etrij.08.0208.0272
  7. G.H.J. Meredith, E.K.Llyod, "The Hamiltonian Graphs 04 to 07," in Combinatorics, D.J.A. Welsh and D.R.Woodal (Eds.), Institute of Mathematics and Applications, Southend-On-Sea pp.229-236, 1972.
  8. P. Fragopoulou and S.G. Akl, "Edge-disjoint spanning trees on the cube connected cycles network," Proc. International Conference on Parallel Processing, vol.1, pp.225-229, 1991.
  9. P.Fraigniaud and C.T.Ho, "Arc-disjoint spanning trees on the cube connected cycles network," Proc. International Conference on Parallel Processing, vol.1, pp.255-229, 1991.
  10. S.L. Johnson and C. T. Ho, "Optimal broadcasting and personalized communication in hypercubes," IEEE Trans. Computers, vol.38, no.9, pp.1249-1268, 1989. https://doi.org/10.1109/12.29465
  11. C.-T.Lin, "Embedding k(n-k) edge-disjoint spanning trees in arrangement graphs," J. Parallel and Distributed Computing, vol.63, pp.1277-1287, 2003. https://doi.org/10.1016/S0743-7315(03)00107-2
  12. W. Shi and P.K. Srimani, "One to all Broadcast in hyper butterfly networks," International Conference on High Performance Computing. pp.155-162, 1998.