Fastest mixing reversible Markov chain on friendship graph: Trade-off between transition probabilities among friends and convergence rate

2019-08-01

Systems & control letters (Print)

AI Summary

This work addresses the fastest-mixing reversible Markov chain problem on friendship graphs, balancing information propagation efficiency (i.e., convergence rate) against structural stability (i.e., constraints on transition probabilities). Methodologically, it integrates spectral graph theory, convex optimization, and symmetry reduction to derive, for the first time, an analytical solution for the fastest-mixing reversible chain on this graph class; via Lagrangian duality, it obtains a closed-form expression for the optimal transition matrix and rigorously characterizes the tight trade-off between spectral gap and transition probabilities. Theoretical contributions include a proven lower bound on mixing time. Empirically, the proposed chain accelerates convergence by over 40% compared to the uniform random walk on typical friendship graphs. The results provide a tractable, verifiable theoretical framework and constructive design methodology for accelerating consensus in structurally constrained networks.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Content-based information diffusion

Problem

• Social Network
• Information Propagation
• Structural Stability

Innovation

• Optimized Hybrid Markov Chain Model
• Centrally-Radiating Network Structure
• Interactive Probability Threshold