自动搜索最优弦环网络族的方法

IF 0.58 Q3 Engineering Journal of Applied and Industrial Mathematics Pub Date : 2024-04-26 DOI:10.1134/s1990478924010113

E. A. Monakhova, O. G. Monakhov

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引用次数: 0

摘要

摘要 Arden 和 Lee 提出了一类阶数为三的弦环网络作为多计算机系统的通信网络，推导出了直径公式，并提出了为其寻找最短路径的分析方法。本文证明，他们提出的直径公式和路由算法是不准确的。我们获得了一个庞大的数据集，其中包含描述所有节点数（最高达 60 000 个）的最佳弦环直径的参数，并找到了弦环网络直径的精确下限。在对数据库进行分析的基础上，我们提出了一种新方法，并实现了自动搜索最优弦环分析描述族的算法。利用该算法，我们找到了 500 多个新的最优弦环网络族的分析描述，适用于多种节点数（迄今为止，文献中只知道六个族）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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来源期刊

Journal of Applied and Industrial Mathematics Engineering-Industrial and Manufacturing Engineering

CiteScore

1.00

自引率

0.00%

发文量

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.