MCR-Tree: An Efficient Index for Multi-dimensional Core Search

Core models are well-known cohesive subgraph models for graph analytics that have been extensively studied. These models, including (α, β)-core, (k, l)-core, and k -core, have multiple parameters, which are referred to as multi-dimensional cores. The goal of core search is to retrieve subgraphs from a graph that satisfy the semantics of a given core model. In the literature, various indexes have been proposed to accelerate core search for different core models. However, existing indexes suffer from several limitations, such as significant redundancy, lack of scalability with respect to the number of parameters, limited generality, and inadequate consideration of index maintenance. To address these limitations, in this paper, we thoroughly investigate the problem of multi-dimensional core search. In particular, we propose a novel index called MCR-Tree, which can be applied to different core models. The MCR-Tree projects all vertices into a multi-dimensional space by leveraging the skyline corenesses, which are indexed by an R-tree. Furthermore, the MCR-Tree integrates the connectivity information of subgraphs into the nodes of the R-tree to facilitate multi-dimensional core search. Subsequently, an efficient branch-and-bound algorithm is designed to perform multi-dimensional core search by traversing the MCR-Tree. Additionally, we discuss how to maintain the MCR-Tree for graph updates. Extensive experiments demonstrate that the MCR-Tree is up to two orders of magnitude smaller than existing indexes and the MCR-Tree-based core search method is up to an order of magnitude faster than existing algorithms.