Accelerating Graph Betweenness Centrality with CUDA

Graph analysis is a fundamental tool for domains as diverse as social networks, computational biology, and machine learning. Real-world applications of graph algorithms involve tremendously large networks that cannot be inspected manually. Betweenness Centrality (BC) is a popular analytic that determines vertex influence in a graph. It has many practical use cases, including finding the best locations for stores within cities, power grid contingency analysis, and community detection. Unfortunately, the fastest known algorithm for computing betweenness centrality has $O(mn)$ time complexity for graphs with $n$ vertices and $m$ edges, making the analysis of large networks challenging.

This post describes how we used CUDA and NVIDIA GPUs to accelerate the BC computation, and how choosing efficient parallelization strategies results in an average speedup of 2.7x, and more than 10x speedup for road networks and meshes versus a naïve edge-parallel strategy.

Betweenness Centrality determines the importance of vertices in a network by measuring the ratio of shortest paths passing through a particular vertex to the total number of shortest paths between all pairs of vertices. Intuitively, this ratio determines how well a vertex connects pairs of vertices in the network. Formally, the Betweenness Centrality of a vertex $v$ is defined as:

$BC(v) = \sum_{s \neq t \neq v} \frac{\sigma_{st}(v)}{\sigma_{st}}$

where $\sigma_{st}$ is the number of shortest paths between vertices $s$ and $t$ and $\sigma_{st}(v)$ is the number of those shortest paths that pass through $v$. Consider Figure 1 above. Vertex 4 is the only vertex that lies on paths from its left (vertices 5 through 9) to its right (vertices 1 through 3). Hence vertex 4 lies on all the shortest paths between these pairs of vertices and has a high BC score. In contrast, vertex 9 does not belong on a path between any pair of the remaining vertices and thus it has a BC score of 0. Continue reading