{"title":"A Method for Automatic Search for Families\nof Optimal Chordal Ring Networks","authors":"E. A. Monakhova, O. G. Monakhov","doi":"10.1134/S1990478924010113","DOIUrl":null,"url":null,"abstract":"<p> Arden and Lee proposed a class of chordal ring networks of degree three as communication\nnetworks for multicomputer systems, derived a formula for the diameter, and produced an\nalgorithm for finding the shortest paths for them. In this paper, it is shown that the formula for\nthe diameter and the routing algorithm presented by them are inaccurate. We have obtained a\nlarge dataset containing parameters for describing optimal diameter chord rings for all the\nnumbers of nodes up to 60 000 and found the exact lower bound for the diameter of chordal ring\nnetworks. A new method is proposed and the algorithms for automatic search for analytical\ndescriptions of families of optimal chordal rings are realized based on an analysis of the database.\nUsing the latter, analytical descriptions of over 500 new families of optimal chordal ring networks\nfor many values of the number of nodes are found (only six families have been known until now in\nthe literature).\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 1","pages":"122 - 136"},"PeriodicalIF":0.5800,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924010113","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
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).
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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