Research Paper#Distributed Systems, Graph Theory, Consensus Algorithms🔬 ResearchAnalyzed: Jan 4, 2026 00:13
Asynchronous Consensus on Dynamic Graphs with Neighborhood Contraction
Published:Dec 25, 2025 15:47
•1 min read
•ArXiv
Analysis
This paper addresses the problem of achieving consensus in a dynamic network where agents update their states asynchronously. The key contribution is the introduction of selective neighborhood contraction, where an agent's neighborhood can shrink after an update, alongside independent changes in other agents' neighborhoods. This is a novel approach to consensus problems and extends existing theory by considering time-varying communication structures with endogenous contraction. The paper's significance lies in its potential applications to evolving social systems and its theoretical contribution to understanding agreement dynamics under complex network conditions.
Key Takeaways
- •Introduces a novel consensus model with asynchronous updates and selective neighborhood contraction.
- •Extends classical consensus theory to time-varying graphs with endogenous contraction.
- •Demonstrates that consensus is achieved almost surely under mild connectivity assumptions.
- •Offers new insights into agreement dynamics in evolving social systems.
Reference
“The system reaches consensus almost surely under the condition that the evolving graph is connected infinitely often.”