Batch Processing for Truss Maintenance in Large Dynamic Graphs

This article studies the batch processing of truss maintenance in large graphs. Trussness is a widely used index in graph analytics for cohesive subgraph mining. It is defined on edges to reflect the closeness of vertices connected by the edges. The trussness maintenance problem, i.e., updating trussness after edge insertions/deletions and avoiding recomputation, was proposed by Cohen (2008) with the assumption that real graphs are continuously evolving in nature and their dynamicity usually only affects few edges. Different from the existing work that mainly focuses on simple single edge/vertex insertion/deletion, we propose batch processing algorithms for truss maintenance with multiedge insertions/deletions. By presenting an edge structure called triangle disjoint set, whose insertion/deletion can make each edge change its trussness by at most 1, we tackle the difficulty in quantifying the trussness changes of the edges in batch processing. More specifically, we propose two indices, namely sustain support and pivotal support, to help measure whether the edges have the potential to change their trussness, such that the search range of the potential edges is greatly reduced. The extensive experiments on real-world graphs illustrate that compared with the single-edge processing approach, our batch processing algorithms can significantly improve the processing efficiency, and the improvement becomes more obvious when more edges are inserted/deleted.