Browse > Article
http://dx.doi.org/10.6109/jkiice.2014.18.5.1110

An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph  

Kim, Jong-Seok (Department of Computer Science, University of Rochester)
Lee, Hyeong-Ok (Department of Computer Education, Sunchon National University)
Publication Information
Journal of the Korea Institute of Information and Communication Engineering / v.18, no.5, 2014 , pp. 1110-1115 More about this Journal
Abstract
The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph $MS_{2,n}$ can be embedded in a transposition graph $T_{2n}$ with dilation n or less and average dilation 2 or less.
Keywords
Algorithm; Interconnection network; Matrix-star graph; One-to-one mapping; Transposition graph;
Citations & Related Records
연도 인용수 순위
  • Reference
1 W. Deng, Q. Luo, "Embedding Complete Binary Trees into Locally Twisted Cubes," Advanced Engineering Forum, vol. 6-7, pp. 70-75, 2012.   DOI
2 J.-S. Kim, M. Kim, H. Sim, and H.-O. Lee, "Embedding Algorithms for Bubble-Sort, Pancake, and Matrix-Star Graphs," Communications in Computer and Information Science, vol. 150, pp. 243-252, 2011.   DOI
3 Z. T. Chou, C. C. Hsu, and J. P. Sheu, "Bubblesort Star graphs: A New Interconnection Network," in Proceedings of the 9th International conference on Parallel and Distributed Systems, pp. 41-48, 1996.
4 H.-O. Lee, H. Sim, J.-H. Seo, and M. Kim, "Embedding Algorithms for Bubble-Sort, Macro-Star, and Transposition Graphs," in Proceedings of the 2010 IFIP international conference on Network and parallel computing, pp. 134-143, 2010.
5 A. Y. Wu, "Embedding of Tree Networks into Hypercubes," Journal of Parallel and Distributed Computing, vol. 2, pp. 238-249, 1985.   DOI   ScienceOn
6 M. Kim, D.-W. Kim, and H.-O. Lee, "Embedding Algorithms for Star, Bubble-Sort, Rotator-Faber-Moore, and Pancake Graphs," in Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing, pp. 348-357, 2010.
7 S. Latifi, P. K. Srimani, "Transposition Networks as a Class of Fault-Tolerant Robust Networks," IEEE Trans. Computers, vol. 45, no. 2, pp. 230-238, 1996.   DOI   ScienceOn
8 S. Ranka, J. Wang, and N. Yeh, "Embedding Meshes on the Star Graph," Journal of Parallel and Distributed Computing, vol. 19, pp. 131-135, 1993.   DOI   ScienceOn
9 S. B. Akers, D. Harel, and B. Krishnamurthy, "The Star Graph: An Attractive Alternative to the n-Cube," in Proceedings of the International Conference on Parallel Processing, pp. 393-400, 1987.
10 H.-O. Lee, J.-S. Kim, K.-W. Park, J.-H. Seo, and E. Oh, "Matrix-Star Graphs: A New Interconnection Network Based on Matrix Operations," in Proceedings of the International Conference on Asia-Pacific Computer Systems Architecture, pp. 478-487, 2005.
11 C. H. Yeh, E. A. Varvarigos, "Macro-Star Networks: Efficient Low-Degree Alternatives to Star Graphs," IEEE Trans. Parallel and Distributed Systems, vol. 9, No. 10, pp. 987-1003, 1998.   DOI   ScienceOn