Nearly Optimal Distributed Algorithm for Computing Betweenness Centrality

Abstract

In this paper, we propose an O(N) time distributed algorithm for computing betweenness centralities of all nodes in the network where N is the number of nodes. Our distributed algorithm is designed under the widely employed CONGEST model in the distributed computing community which limits each message only contains O(log N) bits. To our best knowledge, this is the first linear time deterministic distributed algorithm for computing the betweenness centralities in the published literature. We also give a lower bound for distributively computing the betweenness centrality under the CONGEST model as Ω(D+N/ log N) where D is the diameter of the network. This implies that our distributed algorithm is nearly optimal.