网络设计中最小度与孤立韧度的平衡  

Equilibrium between Minimum Degree and Isolated Toughness in Network Designing

作　　者：朱林立 张海南 高炜[2] ZHU Linli;ZHANG Hainan;GAO Wei(School of Computer Engineering,Jiangsu University of Technology,Changzhou 213001,Jiangsu,China;School of Information Science and Technology,Yunnan Normal University,Kunming 650500,China)

机构地区：[1]江苏理工学院计算机工程学院,江苏常州213001 [2]云南师范大学信息学院,云南昆明650500

出　　处：《昆明理工大学学报(自然科学版)》2025年第2期74-87,共14页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(12161094)。

摘　　要：最小度和孤立韧度是衡量网络易受攻击性的指标.最近的研究发现,这些参数与分数因子的存在性之间存在内在的联系.利用极图理论的方法,对它们的关联进行了进一步的研究,发现在增加最小度下界的情况下,对应孤立韧度的紧界会随之减少,即两个参数之间存在相互平衡的关系.这对网络设计者的参数选择造成了决策困境.为了解决这一问题,将最小度与孤立韧度看成多目标优化问题的帕累托前沿,利用膝盖点计算策略来确定最优参数组合.由于最小度参数在理论上可以无限增加,使得帕累托前沿在该维度上呈现开放性趋势,无法形成封闭的极值点,从而导致传统的膝盖点计算方法无法直接适用于寻找最小度与孤立韧度组合的问题.因此需要引入新的变量ε来刻画孤立韧度的变化,并设计改进的膝盖点计算策略,以确保能够有效识别合理的最优参数组合.The minimum degree and isolated toughness are indicators of network vulnerability.Recent studies have found an inherent relationship between these parameters and the existence of fractional factors.Further study is conducted on their correlation employing extremum graph theory approaches,and it is revealed that by increasing the lower bound of minimum degree,the corresponding tight bound of isolated toughness would decrease,which implies a mutually balanced relationship between these two parameters.This creates a decision-making dilemma for the parameter selection of network designers.To solve this problem,the minimum degree and isolated toughness are considered as Pareto front in multi-objective optimization,and the knee point calculating algorithm is used to determine the optimal parameter combination.Since the minimum degree parameter can theoretically increase indefinitely,the Pareto front exhibits an open-ended trend in this dimension,making it impossible to form a closed extreme point.As a result,traditional knee point calculation methods cannot be directly applied to the problem of finding the combination of minimum degree and isolated toughness.Therefore,it is necessary to introduce a new variable[WTBX]ε[WTBZ]to characterize the variation of isolated toughness and design an improved knee point calculation strategy to ensure the effective identification of reasonable optimal parameter combinations.

关 键 词：网络设计 分数k-因子 孤立韧度 多目标优化 帕累托前沿 

分 类 号：O157.5[理学—数学]