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arXiv · 1506.05783

A Faster Algorithm for Fully Dynamic Betweenness Centrality

Matteo Pontecorvi·Vijaya Ramachandran
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Abstract

We present a new fully dynamic algorithm for maintaining betweenness centrality (BC) of vertices in a directed graph $G=(V,E)$ with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized $O((\nu^*)^2 \log^2 n)$ time per update, where $n = |V| $ and $\nu^*$ bounds the number of distinct edges that lie on shortest paths through any single vertex. This result improves on the amortized bound for fully dynamic BC in [Pontecorvi-Ramachandran2015] by a logarithmic factor. Our algorithm uses new data structures and techniques that are extensions of the method in the fully dynamic algorithm in Thorup [Thorup2004] for APSP in graphs with unique shortest paths. For graphs with $\nu^* = O(n)$, our algorithm matches the fully dynamic APSP bound in [Thorup2004], which holds for graphs with $\nu^* = n-1$, since it assumes unique shortest paths.

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Matteo Pontecorvi, Vijaya Ramachandran. 2015-06-18. A Faster Algorithm for Fully Dynamic Betweenness Centrality. https://arxiv.org/abs/1506.05783

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