New Ring Embedding and its Application into Fault-tolerant Embedding in (n,k)-star Graphs

(n,k)-스타 그래프에서의 새로운 링 임베딩 및 결함허용 임베딩으로의 응용

  • 장정환 (한국전기통신공사 통신망관리센터) ;
  • 좌경룡 (한국과학기술원 전산학과)
  • Published : 2000.03.15

Abstract

In this paper, we consider ring embedding problem on (n,k)-star graphs. We first present a new ring embedding strategy and also prove the superiority in expandability by showing its application into the fault-tolerant ring embedding problem with edge faults. This result can be applied to the multicating applications that use the underlying cycle properties on the multi-computer system.

본 논문에서는 상호연결망 그래프 중 하나인 (n,k)-스타 그래프에 대한 링 임베딩 문제를 다룬다. (n,k)-스타 그래프에 대한 링 임베딩 전략의 유연성을 개선한 새로운 임베딩 기법을 제시하고, 아울러 에지에 결함을 갖는 경우의 결함허용 링 임베딩 문제에 응용 가능함을 보여줌으로써 본 기법의 확장성에서의 우수함을 밝히고자 한다. 본 논문에서 다루고 있는 사이클 특성 관련 연구는 병렬처리 분야에서의 멀티캐스팅 등과 같이 내재된 사이클 특성을 활용하는 분야에 응용이 가능하다.

Keywords

References

  1. F. Berman and L. Snyder, 'On mapping parallel algorithms into parallel architectures,' J of Parallel and Distrib. Comput., Vol.4, pp.439-458, 1987 https://doi.org/10.1016/0743-7315(87)90018-9
  2. B. Monien and H. Sudborough, 'Embedding one interconnection network in another,' Computing Supplement, Vol.7, pp.257-282, 1990
  3. Y. Saad and M. H. Schultz, 'Topological properties of hypercubes,' IEEE Trans. on Comput., Vol.37, pp.867-872, 1988 https://doi.org/10.1109/12.2234
  4. J. H. Park and K. Y. Chwa, 'Recursive circulant: A new topology for multi- computer networks,' Proc. of the Int'l Symp. on Parallel Architectures, Algorithms and Networks, pp.73-80, 1994 https://doi.org/10.1109/ISPAN.1994.367162
  5. S. B. Akers, D. Harel, and B. Krishnamurthy, 'The star graph: An attractive alternative to the n-cube,' Proc. of the Int'l Conf on Parallel Processing, pp.393-400, 1987
  6. K. Day and A. Tripathi, 'A comparative study of topological properties of hypercubes and star graphs,' IEEE Trans. on Paral. and Distrib. Sys., Vol.5, No.1, pp.31-38, 1994 https://doi.org/10.1109/71.262586
  7. J. Misic and Z. Jovanovic, 'Communication aspects of the star graph interconnection network,' IEEE Trans. on Paral. and Distrib. Sys., Vol.5, No.7, pp.678-687, 1994 https://doi.org/10.1109/71.296314
  8. W. K. Chiang and R. J. Chen, 'The (n,k)-star graph: A generalized star graph,' Inf. Process. Lett., Vol. 56, pp.259-264, 1995
  9. J. S. Jwo, S. Lakshmivarahan, and S. K. Dhall, 'Embedding of cycles and grids in star graphs,' Proc. of the Symp. on Parallel and Distrib. Processing, pp.540-547, 1990 https://doi.org/10.1109/SPDP.1990.143600
  10. M. Nigam, S. Sahni, and B. Krishnamurthy, 'Embedding hamiltonians and hypercubes in star interconnection graphs,' Proc. of the Int'l Conf. on Parallel Processing, pp.340-343, 1990
  11. A. Bouabdallah, M. C. Heydemann, and J. Opatrny, 'Embedding complete binary trees into star networks,' Proc. of the Int'l Conf. on Mathematical Foundation of Computer Sci., pp. 266-275, 1994
  12. S. Ranka, J. C. Wang, and N. Yeh, 'Embedding meshes on the star graph,' J. of Parallel and Distrib. Comput., Vol.19, pp.131-135, 1993 https://doi.org/10.1109/SUPERC.1990.130058
  13. W. K. Chiang and R. J. Chen, 'Topological properties of the (n,k)-star graph,' accepted and to appear in Int'l J of Foundations of Computer Sci.
  14. 최혜정, 장직현, '(n,k)-스타 그래프상에서의 인덱싱 기법과 응용', 추계 한국정보과학회 학술지, pp.1731-, 1996
  15. 박천웅, 장직현, '(n,k)-스타 그래프상의 헤밀토니안 임베딩', 한국정보과학회 논문지(A), Vol. 25, No. 12, pp.1384-1391, 1998
  16. Y. C. Tseng, D. K. Panda, and T. H. Lai, 'A trip-based multicasting model in wormhole-routed networks with virtual channels,' IEEE Trans. on Paral. and Distrib. Sys., Vol.7, No.2, pp.138-150, 1996 https://doi.org/10.1109/71.485503