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The Minimum Distance Diagram of Double-Loop Networks
September 2000 (vol. 49 no. 9)
pp. 977-979

Abstract—It is well-known that the minimum distance diagram of a double-loop network yields an L-shape. It is important to know, for a given L-shape, whether there exists a double-loop network realizing it. Necessary and sufficient conditions were given before, but were said to be cumbersome. They also need some clarification. We give new conditions and a simple proof. We also prove that all double-loop networks realizing the same L-shape are isomorphic as the existing proof was given in a Spanish dissertation.

[1] M.A. Fiol, “Applications of Graph Theory to Interconnection Networks,” PhD dissertation, Polytechnic Univ. of Barcelona, Spain, 1982.
[2] M.A. Fiol, M. Valero, J.L.A. Yebra, I. Alegre, and T. Lang, “Optimization of Double-Loop Structures for Local Networks,” Proc. 19th Int'l Symp. MIMI '82, pp. 37-41, 1982.
[3] M.A. Fiol, J.L.A. Yebra, I. Alegre, and M. Valero, “A Discrete Optimization Problem in Local Networks and Data Alignment,” IEEE Trans. Computers, vol. 36, no. 6, pp. 702-713, June 1987.
[4] J. Shen and Q. Li, “Two Theorems on Double-Loop Networks,” unpublished manuscript, 1994.
[5] C.K. Wong and D. Coppersmith, “A Combinatorial Problem Related to Multimodule Organizations,” J. ACM, vol. 21, pp. 392-402, July 1974.

Index Terms:
Double-loop network, L-shape, diameter, sieve method.
Chiuyuan Chen, F.k. Hwang, "The Minimum Distance Diagram of Double-Loop Networks," IEEE Transactions on Computers, vol. 49, no. 9, pp. 977-979, Sept. 2000, doi:10.1109/12.869331
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