The KIPS Transactions:PartA (정보처리학회논문지A)

Korea Information Processing Society (한국정보처리학회)
권호 표지
DOI QR코드

DOI QR Code

A Hamiltonian Property of Pyramid Graphs

피라미드 그래프의 헤밀톤 특성

  • 장정환 (부산외국어대학교 디지털미디어학부)
  • Published : 2006.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we analyze the Hamiltonian property of Pyramid graphs. We prove that it is always possible to construct a Hamiltonian cycle of length $(4^N-1)/3$ by applying the proposed algorithm to construct series of cycle expansion operations into two adjacent cycles in the Pyramid graph of height N.

본 논문에서는 피라미드 그래프에서의 헤밀톤 사이클 특성을 분석한다. 사이클 확장 연산을 이용하여 사이클의 크기를 확대시켜 나가는 일련의 과정을 통하여 헤밀톤 사이클을 찾을 수 있는 제시된 알고리즘을 적용함으로써 임의의 높이 N인 피라미드 그래프 내에 길이 $(4^N-1)/3$인 헤밀톤 사이클이 존재함을 증명한다.

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 https://doi.org/10.1007/978-3-7091-9076-0_13
  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. F. T. Leighton, 'Introduction to Parallel Algorithms and Architectures : Arrays, Trees, Hypercubes,' Morgan. Kaurnmn Pub., CA., 1992
  5. R. Miller and Q. F. Stout, 'Data Movement Techniques for the Pyramid Computer,' SIAM J. on Compui., Vol.16, No.1, pp.38-60, 1987 https://doi.org/10.1137/0216004
  6. Q. F. Stout, 'Mapping Vision Algorithms to Parallel Architectures,' Proc of the IEEE, pp.982-995, 1988 https://doi.org/10.1109/5.5970
  7. D. M. C. Ip, C. K. Y. Ng, L. K. L. Pun, M. Hamdi, and I. Ahmad, 'Embedding Pyramids into 3D Meshes,' Proc. of 1993 Int'l Cont on Parol. and Distrib. Svs., pp.348-352, 1993
  8. K. - L. Chung and Y. - W. Chen, 'Mapping Pyramids into 3-D Meshes,' Nordic J. of Computing, Vol.2, No.3, pp. 326-337, 1995
  9. 장정환,' 피라미드의 3-차원 메쉬로의 신장율 개선 임베딩', 정보처리학회논문지-A. Vol.10-A, No.6, pp.627-634, 2003 https://doi.org/10.3745/KIPSTA.2003.10A.6.627
  10. 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

Cited by

  1. Edge Property of 2n-square Meshes as a Base Graphs of Pyramid Interconnection Networks vol.9, pp.12, 2009, https://doi.org/10.5392/JKCA.2009.9.12.582