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

TL;DR

This paper tackles the Minimum Weighted Vertex Cover problem in fully decentralized networks where nodes rely only on local information. It introduces DecWVC, a local, iterative protocol that uses a gain-based scoring function and an Optimize phase to construct and prune a cover with minimal coordination. Empirical evaluation on 164 graphs and real-world networks shows fast convergence (2–5 rounds), low messaging overhead, and APW close to centralized baselines, demonstrating the practicality of decentralized MWVC. The approach offers scalable, resilient performance for distributed monitoring and resource placement, with future work focusing on asynchronous operation and handling node churn.

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.

Figures (2)

• Figure 1: An example of DecWVC in action. Colored vertex are in the cover set, while bold ones are inactive and not in the cover set. Dashed arrows indicate the $include(\cdot)$ action. Dashed marked arrows indicate the removal of a node
• Figure 2: Messages per node