Hub Labeling for Shortest Path Counting

The notion of shortest path is fundamental in graph analytics. While many works have devoted to devising efficient distance oracles to compute the shortest distance between any vertices s and t, we study the problem of efficiently counting the number of shortest paths between s and t in light of its applications in tasks such as betweenness-related analysis. Specifically, we propose a hub labeling scheme based on hub pushing and discuss several graph reduction techniques to reduce the index size. Furthermore, we prove several theoretical results on the performance of the scheme for some special graph classes. Our empirical study verifies the efficiency and effectiveness of the algorithms. In particular, a query evaluation takes only hundreds of microseconds in average for graphs with up to hundreds of millions of edges. We report our findings in this paper.