Browsing by Author "Lan, James K."

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An efficient algorithm to find a double-loop network that realizes a given L-shape
(2006-08-14)
Chen, Chiuyuan
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Lan, James K.
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Tang, Wen-Shiang
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應用數學系
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電信工程研究所
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.
Constructing independent spanning trees for hypercubes and locally twisted cubes
(2009)
Liu, Yi-Jiun
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Chou, Well Y.
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Lan, James K.
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Chen, Chiuyuan
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應用數學系
Multiple independent spanning trees (ISTs) have applications to fault-tolerant and data broadcasting in interconnections. Thus the designs of multiple ISTs in several classes of networks have been widely investigated. There are two versions of the n ISTs conjecture. The vertex (edge,) conjecture is that any n-connected (n-edge-connected) graph has n vertex-ISTs (edge-ISTs) rooted at an arbitrary vertex r. Note that the vertex conjecture implies the edge conjecture. Recently, Hsieh and Tu proposed an algorithm to construct n edge-ISTs rooted at vertex 0 for the n-dimensional locally twisted cube (LTQ(n)), which is a variant of the n-dimensional hypercube (Q(n)). Since LTQ(n) is not vertex-transitive, Hsieh and Tu's result does not solve the edge conjecture for LTQ(n). In the paper we confirm the vertex conjecture (and hence also the edge conjecture) for LTQ(n) by proposing an algorithm to construct n vertex-ISTs rooted at any vertex. We also confirm the vertex (and also the edge) conjecture for Q(n). To the best of our knowledge, our algorithm is the first algorithm that can construct n vertex-ISTs rooted at any vertex for both LTQ(n) and Q(n).
Constructing independent spanning trees for locally twisted cubes
(2011-05-13)
Liu, Yi-Jiun
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Lan, James K.
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Chou, Well Y.
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Chen, Chiuyuan
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應用數學系
The independent spanning trees (ISTs) problem attempts to construct a set of pairwise independent spanning trees and it has numerous applications in networks such as data broadcasting, scattering and reliable communication protocols. The well-known ISTs conjecture, Vertex/Edge Conjecture, states that any n-connected/n-edge-connected graph has n vertex-ISTs/edge-ISTs rooted at an arbitrary vertex r. It has been shown that the Vertex Conjecture implies the Edge Conjecture. In this paper, we consider the independent spanning trees problem on the n-dimensional locally twisted cube LTQ(n). The very recent algorithm proposed by Hsieh and Tu (2009) [12] is designed to construct n edge-ISTs rooted at vertex 0 for LTQ(n). However, we find out that LTQ(n) is not vertex-transitive when n >= 4; therefore Hsieh and Tu's result does not solve the Edge Conjecture for LTQ(n),,. In this paper, we propose an algorithm for constructing n vertex-ISTs for LTQ(n); consequently, we confirm the Vertex Conjecture (and hence also the Edge Conjecture) for LTQ(n),. (C) 2011 Elsevier B.V. All rights reserved.
Improved upper and lower bounds on the optimization of mixed chordal ring networks
(2009-06-15)
Lan, James K.
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Liu, Victor W.
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Chen, Chiuyuan
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應用數學系
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Department of Applied Mathematics
Recently, Chen, Hwang and Liu [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3-16] introduced the mixed chordal ring network as a topology for interconnection networks. In particular, they showed that the amount of hardware and the network structure of the mixed chordal ring network are very comparable to the (directed) double-loop network, yet the mixed chordal ring network can achieve a better diameter than the double-loop network. More the mixed chordal ring network can achieve diameter about root 2N as compared precisely, to root 3N for the (directed) double-loop network, where N is the number of nodes in the network. One of the most important questions in interconnection networks is, for a given number of nodes, how to find an optimal network (a network with the smallest diameter) and give the construction of such a network. Chen et al. [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3-16] gave upper and lower bounds for such an optimization problem oil the mixed chordal ring network. In this paper, we improve the upper and lower bounds as 2[root N/2] +1 and [root 2N - 3/2], respectively. In addition, we correct some deficient contexts in [S.K. Chen, F.K. Hwang, Y.C. Liu, Some combinatorial properties of mixed chordal rings, J. Interconnection Networks 1 (2003) 3-16]. (C) 2009 Elsevier B.V. All rights reserved.