Search

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 from D$ such that the probability of q$ containing 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. [ABSTRACT FROM PUBLISHER]

Uncertainty is intrinsic to a wide spectrum of real-life applications, which inevitably applies to graph data. Representative uncertain graphs are seen in bio-informatics, social networks, etc. This paper motivates the problem of frequent subgraph mining on single uncertain graphs, and investigates two different - probabilistic and expected - semantics in terms of support definitions. First, we present an enumeration-evaluation algorithm to solve the problem under probabilistic semantics. By showing the support computation under probabilistic semantics is #P-complete, we develop an approximation algorithm with accuracy guarantee for efficient problem-solving. To enhance the solution, we devise computation sharing techniques to achieve better mining performance. Afterwards, the algorithm is extended in a similar flavor to handle the problem under expected semantics, where checkpoint-based pruning and validation techniques are integrated. Experiment results on real-life datasets confirm the practical usability of the mining algorithms. [ABSTRACT FROM AUTHOR]

As the uncertainty is inherent in a wide spectrum of applications such as radio frequency identification (RFID) networks and location-based services (LBS), it is highly demanded to address the uncertainty of the objects. In this paper, we propose a novel indexing structure, named $(U)$-Quadtree, to organize the uncertain objects in the multidimensional space such that the queries can be processed efficiently by taking advantage of $(U)$-Quadtree. Particularly, we focus on the range search on multidimensional uncertain objects since it is a fundamental query in a spatial database. We propose a cost model which carefully considers various factors that may impact the performance. Then, an effective and efficient index construction algorithm is proposed to build the optimal $(U)$-Quadtree regarding the cost model. We show that $(U)$-Quadtree can also efficiently support other types of queries such as uncertain range query and nearest neighbor query. Comprehensive experiments demonstrate that our techniques outperform the existing works on multidimensional uncertain objects. [ABSTRACT FROM PUBLISHER]

Similarity query is a fundamental problem in database, data mining and information retrieval research. Recently, querying incomplete data has attracted extensive attention as it poses new challenges to traditional querying techniques. The existing work on querying incomplete data addresses the problem where the data values on certain dimensions are unknown. However, in many real-life applications, such as data collected by a sensor network in a noisy environment, not only the data values but also the dimension information may be missing. In this work, we propose to investigate the problem of similarity search on dimension incomplete data. A probabilistic framework is developed to model this problem so that the users can find objects in the database that are similar to the query with probability guarantee. Missing dimension information poses great computational challenge, since all possible combinations of missing dimensions need to be examined when evaluating the similarity between the query and the data objects. We develop the lower and upper bounds of the probability that a data object is similar to the query. These bounds enable efficient filtering of irrelevant data objects without explicitly examining all missing dimension combinations. A probability triangle inequality is also employed to further prune the search space and speed up the query process. The proposed probabilistic framework and techniques can be applied to both whole and subsequence queries. Extensive experimental results on real-life data sets demonstrate the effectiveness and efficiency of our approach. [ABSTRACT FROM PUBLISHER]

In this paper, we tackle a novel problem of ranking multivalued objects, where an object has multiple instances in a multidimensional space, and the number of instances per object is not fixed. Given an ad hoc scoring function that assigns a score to a multidimensional instance, we want to rank a set of multivalued objects. Different from the existing models of ranking uncertain and probabilistic data, which model an object as a random variable and the instances of an object are assumed exclusive, we have to capture the coexistence of instances here. To tackle the problem, we advocate the semantics of favoring widely preferred objects instead of majority votes, which is widely used in many elections and competitions. Technically, we borrow the idea from Borda Count (BC), a well-recognized method in consensus-based voting systems. However, Borda Count cannot handle multivalued objects of inconsistent cardinality, and is costly to evaluate top $(k)$ queries on large multidimensional data sets. To address the challenges, we extend and generalize Borda Count to quantile-based Borda Count, and develop efficient computational methods with comprehensive cost analysis. We present case studies on real data sets to demonstrate the effectiveness of the generalized Borda Count ranking, and use synthetic and real data sets to verify the efficiency of our computational method. [ABSTRACT FROM AUTHOR]