In this paper, we investigate the problem of supergraph containment search over uncertain data graphs gu where each edge in a gu has an occurrence probability, namely probabilistic supergraph search, which has a wide spectrum of applications.

Given a query graph$q$, retrieving the data graphs$g$from a set$D$of data graphs such that$q$contains$g$, namely supergraph containment search, is fundamental in graph data analysis with a wide range of real applications. It is very challenging due to the NP-Completeness of subgraph isomorphism testing. Driven by many real applications, in this paper, we study the problem of probabilistic supergraph search; that is, given a set$D$of uncertain data graphs, a certain query graph$q$and a probability threshold$\theta$, we retrieve the data graphs$g^{u}$from$D$such that the probability of$q$containing$g^{u}$is not smaller than$\theta$. We show that besides the NP-Completeness of subgraph isomorphism testing, the problem of calculating probabilities is #P-Complete; thus, it is even more challenging than the supergraph containment search. To tackle the computational hardness, we first propose two novel pruning rules, based on probabilistic connectivity and features, respectively, to efficiently prune non-promising data graphs. Then, efficient verification algorithms are developed with the aim of sharing computation and terminating non-promising computation as early as possible. Extensive performance studies on both real and synthetic data demonstrate the efficiency and effectiveness of our techniques in practice.

Given a query graph $q$ and a data graph G, computing all occurrences of q in G, namely exact all-matching, is fundamental in graph data analysis with a wide spectrum of real applications. It is challenging since even finding one occurrence of q in G (subgraph isomorphism test) is NP-Complete. Consider that in many real applications, exploratory queries from users are often inaccurate to express their real demands. In this paper, we study the problem of efficiently computing all approximate occurrences of q in G. Particularly, we study the problem of efficiently retrieving all matches of q in G with the number of possible missing edges bounded by a given threshold θ, namely similarity all-matching. The problem of similarity all-matching is harder than the problem of exact all-matching since it covers the problem of exact all-matching as a special case with θ = 0.

Uncertain data are inherent in many applications such as environmental surveillance and quantitative economics research. As an important problem in many applications, KNN query has been extensively investigated in the literature. In this paper, we study the problem of processing rank based KNN query against uncertain data. Besides applying the expected rank semantic to compute KNN, we also introduce the median rank which is less sensitive to the outliers. We show both ranking methods satisfy nice top-k properties such as exact-k, containment, unique ranking, value invariance, stability and fairfulness. For given query q, IO and CPU efficient algorithms are proposed in the paper to compute KNN based on expected (median) ranks of the uncertain objects. To tackle the correlations of the uncertain objects and high IO cost caused by large number of instances of the uncertain objects, randomized algorithms are proposed to approximately compute KNN with theoretical guarantees. Comprehensive experiments are conducted on both real and synthetic data to demonstrate the efficiency of our techniques.