Efficient Star-based Truss Maintenance on Dynamic Graphs

Abstract

K-truss is a useful notion of dense subgraphs, which can represent cohesive parts of a graph in a hierarchical way. In practice, in order to enable various truss-based applications to answer queries faster, the edge trussnesses are computed in advance. However, real-world graphs may not always be static and often have edges inserted or removed, leading to costly truss maintenance of recomputing all edge trussnesses. In this paper, we focus on dynamic graphs with star insertions/deletions, where a star insertion can represent a newly joined user with friend connections in social networks or a recently published paper with cited references in citation networks. To tackle such star-based truss maintenance, we propose a new structure of AffBall based on the local structure of an inserted/deleted star motif. With AffBall, we make use of the correlation of inserted edges to compute the trussnesses of the inner edges surrounding the star. Then, we analyze the onion layer of k-truss and conduct truss maintenance for the edges beyond the star, which can be efficiently achieved with a time complexity related to the number of the edges that change the onion layer. Moreover, we extend star-based truss maintenance to handle general updates and single-edge insertions/deletions. Extensive experiments on real-world dynamic graphs verify the effectiveness and efficiency of proposed algorithms against state-of-the-art truss maintenance algorithms.