Reliable Community Search on Uncertain Graphs
Xiaoye Miao, Yue Liu, Lu Chen, Yunjun Gao, Jianwei Yin
Abstract
Community search (CS) on graphs returns the largest densely connected vertex subset containing a query vertex, namely k-community, where every vertex's degree in the induced subgraph is not less than <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> . It has significant influence in many real-life applications including event organization and friend recommendation. Many complex networks such as social networks and protein-protein interaction (PPI) networks are often modeled as uncertain graphs. In this paper, we identify and study the problem of reliable community search on uncertain graphs (UCS for short). Given an uncertain graph, a query vertex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> , a positive integer <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> and a probability threshold θ, the reliable community, viz., (k, θ) -community, of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> is the largest vertex subset, so that the probability of every vertex to be in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> 's k-community is not less than θ. We prove that it is a NP-hard problem. We propose two novel pruning strategies to reduce the candidate set to a much smaller size. We develop an efficient index, namely CD-index, with which the pruning process can be done in optimal time. We also present efficient sampling algorithms on top of stratified sampling and lazy sampling to accelerate the search under accuracy guarantees. Extensive experiments using four real-world datasets demonstrate the superior performance of proposed algorithms to the state-of-the-art approaches.