Double loop networks with minimum delay
Discrete Mathematics
Discrete Optimization Problem in Local Networks and Data Alignment
IEEE Transactions on Computers
Diameters of weighted double loop networks
Journal of Algorithms
Double commutative-step digraphs with minimum diameters
Discrete Mathematics - Special issue on combinatorics and algorithms
An efficient algorithm to find optimal double loop networks
Selected papers of the 14th British conference on Combinatorial conference
Distributed loop computer networks: a survey
Journal of Parallel and Distributed Computing
Weighted multi-connected loop networks
Discrete Mathematics
An optimal message routing algorithm for double-loop networks
Information Processing Letters
A Combinatorial Problem Related to Multimodule Memory Organizations
Journal of the ACM (JACM)
A dynamic fault-tolerant message routing algorithm for double-loop networks
Information Processing Letters
A complementary survey on double-loop networks
Theoretical Computer Science
Survival Reliability of Some Double-Loop Networks and Chordal Rings
IEEE Transactions on Computers
An efficient algorithm to find a double-loop network that realizes a given L-shape
Theoretical Computer Science
Analysis of Chordal Ring Network
IEEE Transactions on Computers
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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 precisely, the mixed chordal ring network can achieve diameter about 2N as compared to 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 on the mixed chordal ring network. In this paper, we improve the upper and lower bounds as 2@?N/2@?+1 and @?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].