Decision making strategy for δ − I equilibrium problem in network designing

¹ School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, PR China
² School of Software Engineering, South China University of Technology, Guangzhou 510000, PR China
³ School of Mathematics, Hohai University, Nanjing 211100, PR China

^* Corresponding author: gaowei@hhu.edu.cn

Received: 20 August 2023
Accepted: 25 September 2025

Abstract

The existence of fractional factors characterizes the fractional flows in a network, and hence indirectly characterizes the feasibility of data transmission. The minimum degree and isolated toughness characterize network topology from the perspectives of sparsity and stability, which serves as the theoretical conditions for fractional factors. This article reveals from a theoretical perspective that if the minimum degree condition increases, the corresponding tight isolated toughness variant bound will decrease. This infinite number of parameter combinations cause a “choice dilemma” for decision-makers. To solve this problem, we regard these two parameters as the Pareto front of the bi-objective optimization problem, and a knot point calculation approach is designed to determine the optimal combination.