Fast Core Maintenance in Dynamic Graphs

This article studies the core maintenance problem in dynamic graphs. The core number is a fundamental index reflecting the cohesiveness of a graph, which is widely used in large-scale graph analytics. The core maintenance problem requires updating the core numbers of vertices after a set of edges and vertices are inserted into or deleted from the graph. Previous works focus on the scenario of single-edge updates and process the edges one by one when multiple edges are inserted/deleted. We initiate the studies of processing multiple edges concurrently to improve the efficiency of core maintenance. Specifically, we discover a structure of inserted/deleted edges,
superior edge set
, which can be processed together to greatly reduce unnecessarily repeated visits of vertices in the procedure of sequential edge processing. Based on the structure of the superior edge set, efficient algorithms are then devised for incremental and decremental core maintenance, respectively. Compared with single-edge processing algorithms, our algorithms show a significant speedup in the processing time. Furthermore, our algorithms admit parallel implementations, which can further improve the update efficiency. We also conduct extensive experiments on different types of real-world, temporal, and synthetic data sets, and the results illustrate that the proposed algorithms exhibit good efficiency, stability, and scalability.