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Graphs are prevailingly used in many applications to model complex data structures. In this paper, we study the problem of supergraph containment search. To avoid the NP-complete subgraph isomorphism test, most existing works follow the filtering-verification framework and select graph-features to build effective indexes, which filter false results (graphs) before conducting the costly verification. However, searching features multiple times in the query graphs yields huge redundant computation, which leads to the emergence of the computation-sharing framework. This paper follows the roadmap of computation-sharing framework to efficiently process supergraph containment queries. Firstly, database graphs are clustered into disjoint groups for sharing the computation cost within each group. While it is shown NP-hard to maximize the computation-sharing benefits of a clustering, efficient algorithm is developed to approximate the optimal solution with an approximation factor of 1 2. A novel prefix-sharing indexing technique, PrefIndex, is then proposed based on which efficient query processing algorithm integrating both filtering and verification is developed. Finally, PrefIndex is enhanced with multi-level sharing and suffix-sharing to further avoid redundant computation. An extensive empirical study demonstrates the efficiency and scalability of our techniques which achieve orders of magnitudes of speed-up against the state-of-the-art techniques.

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Abstract. Reachability query is a fundamental problem in graph databases. It answers whether or not there exists a path between a source vertex and a destination vertex and is widely used in various applications including road networks, social networks, world wide web and bioinformatics. In some emerging important applications, uncertainties may be inherent in the graphs. For instance, each edge in a graph could be associated with a probability to appear. In this paper, we study the reachability problem over such uncertain graphs in a threshold fashion, namely, to determine if a source vertex could reach a destination vertex with probabilty larger than a user specified probability value t. Finding reachability on uncertain graphs has been proved to be NP-Hard. We first propose novel and effective bounding techniques to obtain the upper bound of reachability probability between the source and destination. If the upper bound fails to prune the query, efficient dynamic Monte Carlo simulation technqiues will be applied to answer the probabilitistic reachability query with an accuracy guarantee. Extensive experiments over real and synthetic datasets are conducted to demonstrate the efficiency and effectiveness of our techniques.

Abstract-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 exactk, 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.