Construction of Dual Optimal Bidirectional Double-Loop Networks for Optimal Routing

Hui Liu, Xiaowan Li and Shenling Wang ()
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Hui Liu: School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China
Xiaowan Li: School of Computer Science and Technology, An Hui University of Technology, Maanshan 243002, China
Shenling Wang: School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China

Mathematics, 2022, vol. 10, issue 21, 1-17

Abstract: Bidirectional double-loop networks (BDLNs) are widely used in computer networks for their simplicity, symmetry and scalability. One common way to improve their performance is to decrease the diameter and average distance. Attempts have been made to find BDLNs with minimal diameters; however, such BDLNs will not necessarily have the minimum average distance. In this paper, we construct dual optimal BDLNs with minimum diameters and average distances using an efficient method based on coordinate embedding and transforming. First, we get the lower bounds of both the diameter and average distance by embedding a BDLN into Cartesian coordinates. Then, we construct tight optimal BDLNs that provide the aforementioned lower bounds based on an embedding graph. On the basis of node distribution regularity in tight optimal BDLNs, we construct dual optimal BDLNs with minimum diameters and average distances for any number of nodes. Finally, we present on-demand optimal message routing algorithms for the dual optimal BDLNs that we have constructed. The presented algorithms do not require routing tables and are efficient, requiring little computation.

Keywords: bidirectional double-loop networks; diameter; average distance; lower bound; optimal routing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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