A lightweight, system-wide global termination detection algorithm that enables vertices to decide locally when the overall system has converged, and emphasises the need for coordinated halting in distributed centrality computation.
Abstract
Computing betweenness centrality on large networks is inherently expensive, as it requires aggregating shortest-path dependencies across all pairs of vertices and becomes increasingly difficult to scale as network size grows. Scalable distributed algorithms can facilitate such computations, particularly when centralised processing is not feasible, and message exchanges must be carefully controlled, for example, in bandwidth-limited or very large-scale networks. However, existing distributed betweenness centrality implementations do not integrate a lightweight, system-wide termination detector. As a consequence, this can lead to extra messaging after local convergence or, if misconfigured, premature stops. In this work, a lightweight, system-wide global termination detection algorithm for this task is presented. The proposed method enables vertices to decide locally when the overall system has converged. The method is evaluated against a local stopping strategy in which vertices terminate individually once their own estimates stabilise. To compare these two approaches, namely global termination detection and local stopping, a custom Python simulator is implemented, and both approaches are tested on synthetic (Erdos-Renyi and geometric) and real (Email and Road) network topologies. Our results show that system-wide termination detection lets vertices stop safely after detecting global convergence, as indicated by zero final error in the evaluated networks, rather than stopping independently based only on local convergence. The local stopping approach, on the other hand, results in premature termination and some errors on heterogeneous networks. This work emphasises the need for coordinated halting in distributed centrality computation.
Betweenness centrality quantifies a node's influence on information spread. While classical shortest-path metrics ignore path redundancy, random walk betweenness centrality considers all possible routes but over-emphasizes circuitous ones. To bridge these extremes, interpolated measures offer a tunable continuum between efficiency and randomness. In this paper, we propose a unified distributed framework for calculating interpolated betweenness centrality under the CONGEST model, where nodes have local knowledge and limited $O(\log n)$ bandwidth. Our framework accommodates different interpolation logics, such as path pruning and target biasing. By leveraging a parallelized randomized sampling mechanism to provide approximate estimations, our algorithm achieves a round complexity of $O(n \log n)$. Experimental results demonstrate the algorithm's scalability in distributed large-scale networks, showing that a satisfactory approximation ratio can be achieved given a sufficiently large sample size.
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