Fully Dynamic Shortest-Path Distance Query Acceleration on Massive Networks

The distance between vertices is one of the most fundamental measures for representing relations between them, and it is the basis of other classic measures of vertices, such as similarity, centrality, and influence. The 2-hop labeling methods are known as the fastest exact point-to-point distance algorithms on million-scale networks. However, they cannot handle billion-scale networks because of the large space requirement and long preprocessing time. In this paper, we present the first algorithm that can process exact distance queries on fully dynamic billion-scale networks besides trivial non-indexing algorithms, which combines an online bidirectional breadth-first search (BFS) and an offline indexing method for handling billion-scale networks in memory. First, we accelerate bidirectional BFSs by using heuristics that exploit the small-world property of complex networks. Then, we construct bit-parallel shortest-path trees to maintain sets of shortest paths passing through high-degree vertices of networks in compact form, the information of which enables us to avoid visiting vertices with high degrees during bidirectional BFSs. Thus, the searches achieve considerable speedup. In addition, our index size reduction technique enables us to handle billion-scale networks in memory. Furthermore, we introduce dynamic update procedures of our data structure to handle fully dynamic networks. We evaluated the performance of the proposed method on real-world networks. In particular, on large-scale social networks with over 1B edges, the proposed method enables us to answer distance queries in around 1 ms, on average.