On Time-optimal (k, p)-core Community Search in Dynamic Graphs

Abstract

Community search aims to find cohesive subgraphs containing certain vertices, attracting increasing interest recently. However, existing cohesive models such as k-core mainly focus on the dense connections inside the community, and neglect the interactions with the vertices outside. In this paper, we study the (k,p) -core community search (KPCS) problem in dynamic graphs, i.e., find the maximal connected subgraph containing a query vertex where each vertex has at least k neighbors and at least p fraction of its neighbors in the subgraph. Such fraction and connectivity constraints bring non-trivial challenges to the online community search in dynamic graphs. Thus, we design a space-efficient <tex>$O(m)$</tex> where <tex>$m$</tex> is the edge number) index KPForest which can support time-optimal (k,p) -core community search. We also propose novel construction and maintenance algorithms to record and update the (k,p) value and the connectivity information for dynamic graphs correctly and efficiently. Extensive experimental studies on ten real-world datasets show that our index can support community search with two orders of magnitude speedup at a small cost of construction and maintenance compared with the baseline algorithms.