Galliot: Path Merging Based Betweenness Centrality Algorithm on GPU

Betweenness centrality (BC) is widely used to measure a vertex’s significance by using the frequency of a vertex appearing in the shortest path between other vertices. However, most recent algorithms in BC computation suffer from the problem of high auxiliary memory consumption. To reduce BC computing’s memory consumption, we propose a path-mergingbased algorithm called Galliot to calculate the BC values on GPU, which aims to minimize the on-board memory consumption and enable the BC computation of large-scale graphs. The proposed algorithm requires $\mathcal{O}$(n) space and runs in $\mathcal{O}$(mn) time on unweighted graphs. We present the theoretical principle for the proposed path merging method. Moreover, we propose a locality-oriented policy to maintain and update the worklist to improve GPU data locality. In addition, we conducted extensive experiments on NVIDIA GPUs to show the performance of Galliot. The results show that Galliot can process the larger graphs, which have 11.32× more vertices and 5.67× more edges than the graphs that recent works. Moreover, Galliot can achieve up to 38.77× speedup over the existing methods.

I. Introduction

Betweenness centrality (BC) is one of the most important measures for a graph. BC is firstly proposed to measure the importance of particular vertices in the social networks [1]. This paper use G = (V,E) to express a graph, where V and E are the vertex and edge set of G. There is a path between vertex u and v if there is a vertex series that is connected by edges. The betweenness of a particular vertex v represents the number of the shortest paths between all pairs of vertices passing through v. If we use σ_st to denote the number of shortest paths between vertex s and t, and σ_st(v) to represent the number of the shortest paths from s to t that go through vertex v, then the BC score of v can be calculated by formula (1). A high BC score indicates a high probability that the vertex lies on the shortest path, which indicates the graph will crash once we delete this vertex. The BC score plays a pivotal role in many industrial and academic applications, such as social network analysis [2], computer networks [3], and many other applications that use graphs as their data models [4].