Computing Exact Vertex Eccentricity on Massive-Scale Distributed Graphs

The eccentricity of a vertex is defined as the length of the longest shortest path to any other vertex. While eccentricity is an important measure of vertex centrality, directly computing exact eccentricity for all vertices on large-scale graphs is prohibitively costly. Takes and Kosters proposed an iterative algorithm that uses multiple runs of single-source shortest path (SSSP) to compute lower and upper bounds on eccentricity at every vertex. Their technique converges to exact eccentricity by performing SSSP from only a small percentage of vertices, when sources are efficiently selected. However, their source selection strategies do not always yield rapid convergence. We propose a pincer movement source selection algorithm that efficiently selects source vertices based on analysis of the lower and upper bounds produced by SSSP. We also leverage k-BFS, which runs breadth-first search (BFS) from multiple sources concurrently on HavoqGT, a high-performance vertex-centric message-passing graph processing framework, to achieve an additional significant performance improvement on distributed-memory systems. We demonstrate that our novel source vertex selection strategy has better performance on various real-world graph datasets compared with the previous strategy. In addition, we compute exact eccentricity for graphs with more than 1000X more edges (112B undirected edges) than graphs in the previous literature.