Title: An efficient algorithm to find a double-loop network that realizes a given L-shape
Authors: Chen, Chiuyuan
Lan, James K.
Tang, Wen-Shiang
Department of Applied Mathematics
Institute of Communications Engineering
Keywords: local area network;double-loop network;diameter;L-shape;algorithm
Issue Date: 14-Aug-2006
Abstract: Double-loop networks have been widely studied as an architecture for local area networks. It is well known that the minimum distance diagram of a double-loop network yields an L-shape. Given a positive integer N, it is desirable to find a double-loop network with its diameter being the minimum among all double-loop networks with N nodes. Since the diameter of a double-loop network can be easily computed from its L-shape, one method is to start with a desirable L-shape and then find a double-loop network to realize it. This is a problem discussed by many authors [F Aguilo, M.A. Fiol, An efficient algorithm to find optimal double loop networks, Discrete Math. 138 (1995) 15-29, R.C. Chan, C.Y. Chen, ZX Hong, A simple algorithm to find the steps of double-loop networks, Discrete Appl. Math. 121 (2002) 61-72, C.Y. Chen, F.K. Hwang, The minimum distance diagram of double-loop networks, IEEE Trans. Comput. 49 (2000) 977-979, P. Esque, F Aguilo, M.A. Fiol, Double commutative-step diagraphs with minimum diameters, Discrete Math. 114 (1993) 147-157] and it has been open for a long time whether this problem can be solved in O(log N) time. In this paper, we will provide a simple and efficient 0 (log N)-time algorithm for solving this problem. (C) 2006 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.tcs.2006.01.048
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2006.01.048
Volume: 359
Issue: 1-3
Begin Page: 69
End Page: 76
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