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A Method for Automatic Search for Families of Optimal Chordal Ring Networks

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Abstract

Arden and Lee proposed a class of chordal ring networks of degree three as communication networks for multicomputer systems, derived a formula for the diameter, and produced an algorithm for finding the shortest paths for them. In this paper, it is shown that the formula for the diameter and the routing algorithm presented by them are inaccurate. We have obtained a large dataset containing parameters for describing optimal diameter chord rings for all the numbers of nodes up to 60 000 and found the exact lower bound for the diameter of chordal ring networks. A new method is proposed and the algorithms for automatic search for analytical descriptions of families of optimal chordal rings are realized based on an analysis of the database. Using the latter, analytical descriptions of over 500 new families of optimal chordal ring networks for many values of the number of nodes are found (only six families have been known until now in the literature).

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Funding

This research was carried out within framework of state assignment of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences under agreement no. FWNM–2022–0005.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    E. A. Monakhova & O. G. Monakhov

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  1. E. A. Monakhova
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  2. O. G. Monakhov
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Correspondence to E. A. Monakhova or O. G. Monakhov.

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Translated by V. Potapchouck

CONFLICT OF INTEREST. The authors of this work declare that they have no conflicts of interest.

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Monakhova, E.A., Monakhov, O.G. A Method for Automatic Search for Families of Optimal Chordal Ring Networks. J. Appl. Ind. Math. 18, 122–136 (2024). https://doi.org/10.1134/S1990478924010113

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  • DOI: https://doi.org/10.1134/S1990478924010113

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