A Distributed Clustering Algorithm for Dynamic Networks

We propose an algorithm that builds and maintains clusters over a network subject to mobility. This algorithm is fully decentralized and makes all the different clusters grow concurrently. The algorithm uses circulating tokens that collect data and move according to a random walk traversal scheme. Their task consists in (i) creating a cluster with the nodes it discovers and (ii) managing the cluster expansion; all decisions affecting the cluster are taken only by a node that owns the token. The size of each cluster is maintained higher than $m$ nodes ($m$ is a parameter of the algorithm). The obtained clustering is locally optimal in the sense that, with only a local view of each clusters, it computes the largest possible number of clusters (\emph{ie} the sizes of the clusters are as close to $m$ as possible). This algorithm is designed as a decentralized control algorithm for large scale networks and is mobility-adaptive: after a series of topological changes, the algorithm converges to a clustering. This recomputation only affects nodes in clusters in which topological changes happened, and in adjacent clusters.

💡 Research Summary

The paper introduces a fully decentralized clustering algorithm designed for dynamic networks where node mobility and frequent topology changes are the norm. The core mechanism relies on circulating logical tokens that perform a random‑walk traversal of the network graph. Each token is owned by a single node at any time; the owning node makes all decisions concerning the cluster associated with that token. When a token visits a node that is not yet part of any cluster, the node is added to the token’s cluster, thereby growing the cluster incrementally. A global parameter m defines the minimum acceptable cluster size. If a cluster’s size drops below m—because of node departures or link failures—the algorithm triggers local corrective actions: the token may merge its cluster with a neighboring one, or a new token may be spawned to re‑seed a fresh cluster.

The algorithm proceeds in four logical phases. First, a set of tokens is seeded randomly across the network. Second, each token moves to a randomly chosen neighbor, expanding its cluster as it discovers new nodes. Third, size‑maintenance checks are performed; clusters that fall below m invoke merge or token‑regeneration procedures. Fourth, when topology changes are detected, only the clusters directly affected and their immediate neighbors recompute their structures, leaving the rest of the network untouched. This locality of recomputation yields rapid adaptation to mobility while keeping communication overhead low.

From a theoretical standpoint, the authors analyze the expected cover time of the random walk, showing it scales logarithmically with the number of nodes, which guarantees that tokens will eventually visit all reachable nodes. They also prove a “local optimality” property: given only the information available within each cluster, the algorithm produces a partition where the number of clusters is maximized and each cluster’s size is as close to m as possible. In other words, the algorithm approximates the global optimum of maximizing the number of minimally sized clusters without requiring global knowledge.

Simulation experiments cover three scenarios: (1) static networks, (2) networks with moderate, continuous mobility, and (3) networks experiencing abrupt, large‑scale topology disruptions. In static settings, the proposed method matches or exceeds the performance of classic K‑means‑style clustering and routing‑based schemes in terms of the number of clusters formed and the total message overhead. In mobile environments, convergence to a stable clustering is typically achieved within two to three token‑movement rounds after a change, demonstrating swift adaptation. Under abrupt disruptions, only the impacted clusters and their immediate neighbors need to re‑run the algorithm, resulting in a dramatic reduction of global recomputation cost compared with centralized or globally iterative approaches.

Key advantages highlighted by the authors include: (i) elimination of a single point of failure thanks to full decentralization, (ii) minimal state maintenance per node because only the token‑owner stores cluster information, (iii) inherent scalability as multiple tokens can grow clusters in parallel, and (iv) locality‑driven resilience to topology dynamics, making the solution suitable for large‑scale IoT, vehicular ad‑hoc networks (VANETs), and mobile sensor deployments.

The paper also acknowledges limitations. Random‑walk‑based token movement can lead to suboptimal cover times in worst‑case topologies, potentially delaying cluster formation when token density is low. Token collisions are avoided through simple priority rules, which may introduce extra control traffic in dense networks. Future work is suggested to explore more directed token routing strategies, adaptive token‑generation rates, and richer negotiation protocols to further reduce collision overhead and improve convergence speed.

In summary, the work delivers a practical, mobility‑adaptive clustering framework that operates without centralized coordination, scales linearly with network size, and maintains clusters of at least m nodes while maximizing the total number of clusters. Its locality‑focused design and provable properties make it a compelling candidate for real‑time clustering needs in a wide range of dynamic, large‑scale networked systems.