Efficient Algorithm for Maximizing Betweenness Centrality in Large Networks

Betweenness centrality captures the importance of a vertex by quantifying the number of times it is traversed as part of the shortest path between other vertices. Betweenness centrality maximization is a fundamental task in network analysis with a wide range of applications. Specifically, given a network
$G$
and a positive integer
$k$
, this problem aims to find a set with
$k$
vertices that has the maximum betweenness centrality. Previous research has investigated different techniques for approximating betweenness centrality maximization with near-linear time complexity. Despite the theoretical guarantees that minimize the sample size, computing the betweenness centrality of all vertices can still be time-consuming, particularly for large graphs. In this paper, we propose a novel algorithm, BKBWC, for maximizing the betweenness centrality of a set of
$k$
vertices in a network. Our method utilizes the bottom-k sketch to enable early termination when the seed set size meets
$k$
, significantly accelerating the algorithm while maintaining accuracy. We demonstrate the efficiency and accuracy of our method on 10 real-world datasets, showing that our algorithm achieves 30x speedup compared with the state-of-the-art approach HEDGE, while still producing results comparable to exact methods in terms of accuracy.