Efficient Maintenance of Distance Labelling for Incremental Updates in Large Dynamic Graphs (2102.08529v1)

Abstract: Finding the shortest path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has been successfully attempted on this problem, most of which is limited to static graphs. Due to the dynamic nature of real-world networks, there is a pressing need to address this problem for dynamic networks undergoing changes. In this paper, we propose an \emph{online incremental} method to efficiently answer distance queries over very large dynamic graphs. Our proposed method incorporates incremental update operations, i.e. edge and vertex additions, into a highly scalable framework of answering distance queries. We theoretically prove the correctness of our method and the preservation of labelling minimality. We have also conducted extensive experiments on 12 large real-world networks to empirically verify the efficiency, scalability, and robustness of our method.