Fast Computation and Optimization for Opinion-Based Quantities of Friedkin-Johnsen Model

2026-06-25

AI Summary

This work addresses the computational inefficiency in evaluating key quantities such as opinion polarization and disagreement within the Friedkin–Johnsen model. To overcome this limitation, the authors propose a novel algorithm based on partial rooted forests. By leveraging the structural properties of partial rooted forests and integrating graph-theoretic insights with randomized sampling techniques, the approach reduces the time complexity of related optimization tasks—including minimizing opinions, polarization, and disagreement—from linear to sublinear. The method achieves high accuracy while significantly enhancing scalability on large-scale networks. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art methods in both efficiency and effectiveness.

Abstract

In this paper, we address the problem of fast computation and optimization of opinion-based quantities in the Friedkin-Johnsen (FJ) model. We first introduce the concept of partial rooted forests, based on which we present an efficient algorithm for computing relevant quantities using this method. Furthermore, we study two optimization problems in the FJ model: the Opinion Minimization Problem and the Polarization and Disagreement Minimization Problem. For both problems, we propose fast algorithms based on partial rooted forest samplings. Our methods reduce the time complexity from linear to sublinear. Extensive experiments on real-world networks demonstrate that our algorithms are both accurate and efficient, outperforming state-of-the-art methods and scaling effectively to large-scale networks.

Problem

• Friedkin-Johnsen model
• opinion minimization
• polarization minimization
• disagreement minimization
• opinion dynamics

Innovation

• partial rooted forests
• Friedkin-Johnsen model
• sublinear time algorithm
• opinion optimization
• polarization minimization