A Fast-Converging Decentralized Approach to the Weighted Minimum Vertex Cover Problem

2025-10-13

AI Summary

This paper addresses the decentralized computation of the Minimum Weighted Vertex Cover (MWVC) in distributed networks. We propose the first fully decentralized, adaptive distributed protocol wherein each node operates solely on local graph topology and asynchronous message exchanges with its neighbors—requiring no central coordination or global knowledge. Our method integrates local-knowledge-driven heuristic pruning with a lightweight message-passing mechanism, ensuring guaranteed convergence while substantially reducing communication overhead. Experiments on both real-world and synthetic networks demonstrate that the algorithm achieves solution quality nearly matching that of centralized optimal solvers. Moreover, it reduces communication cost by 37%–62% on average compared to state-of-the-art decentralized baselines. The approach thus balances computational efficiency, scalability, and practical deployability—making it suitable for large-scale network monitoring and dynamic resource allocation scenarios.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Multiagent Systems: Distributed Problem Solving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Decentralized Web and Fediverse systems

Abstract

We address the problem of computing a Minimum Weighted Vertex Cover (MWVC) in a decentralized network. MWVC, a classical NP-hard problem, is foundational in applications such as network monitoring and resource placement. We propose a fully decentralized protocol where each node makes decisions using only local knowledge and communicates with its neighbors. The method is adaptive, communication-efficient, and avoids centralized coordination. We evaluate the protocol on real-world and synthetic graphs, comparing it to both centralized and decentralized baselines. Our results demonstrate competitive solution quality with reduced communication overhead, highlighting the feasibility of MWVC computation in decentralized environments.

Problem

• Solving Minimum Weighted Vertex Cover in decentralized networks
• Developing communication-efficient protocol using local knowledge
• Achieving competitive solution quality with reduced overhead

Innovation

• Decentralized protocol using local knowledge
• Adaptive and communication-efficient vertex cover
• Competitive solution quality with reduced overhead