A Highly Scalable Labelling Approach for Exact Distance Queries in Complex Networks

Answering exact shortest path distance queries is a fundamental task in graph theory. Despite a tremendous amount of research on the subject, there is still no satisfactory solution that can scale to billion-scale complex networks. Labelling-based methods are well-known for rendering fast response time to distance queries; however, existing works can only construct labelling on moderately large networks (million-scale) and cannot scale to large networks (billion-scale) due to their prohibitively large space requirements and very long preprocessing time. In this work, we present novel techniques to efficiently construct distance labelling and process exact shortest path distance queries for complex networks with billions of vertices and billions of edges. Our method is based on two ingredients: (i) a scalable labelling algorithm for constructing minimal distance labelling, and (ii) a querying framework that supports fast distance-bounded search on a sparsified graph. Thus, we first develop a novel labelling algorithm that can scale to graphs at the billion-scale. Then, we formalize a querying framework for exact distance queries, which combines our proposed highway cover distance labelling with distance-bounded searches to enable fast distance computation. To speed up the labelling construction process, we further propose a parallel labelling method that can construct labelling simultaneously for multiple landmarks. We evaluated the performance of the proposed methods on 12 real-world networks. The experiments show that the proposed methods can not only handle networks with billions of vertices, but also be up to 70 times faster in constructing labelling and save up to 90\% of labelling space. In particular, our method can answer distance queries on a billion-scale network of around 8B edges in less than 1ms, on average.