In this paper we introduce and experimentally compare alternative algorithms to join uncertain relations. Different algorithms are based on specific principles, e.g., sorting, indexing, or building intermediate relational tables to apply traditional approaches. As a consequence their performance is affected by different features of the input data, and each algorithm is shown to be more efficient than the others in specific cases. In this way statistics explicitly representing the amount and kind of uncertainty in the input uncertain relations can be used to choose the most efficient algorithm.
Probabilistic joins are useful when objects may match , differently from our work where we compute exact joins and the additional workload depends on our ignorance of the real values we are manipulating. These approximate probabilistic joins have been studied in @cite_3 , dealing with joins between similar objects, and @cite_7 , focusing on nearest-neighbor joins.
@cite_7 @cite_3
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An important database primitive for commonly used feature databases is the similarity join. It combines two datasets based on some similarity predicate into one set such that the new set contains pairs of objects of the two original sets. In many different application areas, e.g. sensor databases, location based services or face recognition systems, distances between objects have to be computed based on vague and uncertain data. In this paper, we propose to express the similarity between two uncertain objects by probability density functions which assign a probability value to each possible distance value. By integrating these probabilistic distance functions directly into the join algorithms the full information provided by these functions is exploited. The resulting probabilistic similarity join assigns to each object pair a probability value indicating the likelihood that the object pair belongs to the result set. As the computation of these probability values is very expensive, we introduce an efficient join processing strategy exemplarily for the distance-range join. In a detailed experimental evaluation, we demonstrate the benefits of our probabilistic similarity join. The experiments show that we can achieve high quality join results with rather low computational cost. Spatial join is an expensive operation that is commonly used in spatial database systems. In order to generate efficient query plans for the queries involving spatial join operations, it is crucial to obtain accurate selectivity estimates for these operations. In this paper we introduce a framework for estimating the selectivity of spatial joins constrained by geometric selections. The center piece of the framework is Euler Histogram, which decomposes the estimation process into estimations on vertices, edges and faces. Based on the characteristics of different datasets, different probabilistic models can be plugged into the framework to provide better estimation results. To demonstrate the effectiveness of this framework, we implement it by incorporating two existing probabilistic models, and compare the performance with the Geometric Histogram [1] and the algorithm recently proposed by Mamoulis and Papadias. In emerging applications such as location-based services, sensor monitoring and biological management systems, the values of the database items are naturally imprecise. For these uncertain databases, an important query is the Probabilistic k-Nearest-Neighbor Query (k-PNN), which computes the probabilities of sets of k objects for being the closest to a given query point. The evaluation of this query can be both computationally- and I O-expensive, since there is an exponentially large number of k object-sets, and numerical integration is required. Often a user may not be concerned about the exact probability values. For example, he may only need answers that have sufficiently high confidence. We thus propose the Probabilistic Threshold k-Nearest-Neighbor Query (T-k-PNN), which returns sets of k objects that satisfy the query with probabilities higher than some threshold T. Three steps are proposed to handle this query efficiently. In the first stage, objects that cannot constitute an answer are filtered with the aid of a spatial index. The second step, called probabilistic candidate selection, significantly prunes a number of candidate sets to be examined. The remaining sets are sent for verification, which derives the lower and upper bounds of answer probabilities, so that a candidate set can be quickly decided on whether it should be included in the answer. We also examine spatially-efficient data structures that support these methods. Our solution can be applied to uncertain data with arbitrary probability density functions. We have also performed extensive experiments to examine the effectiveness of our methods. In applications like location-based services, sensor monitoring and biological databases, the values of the database items are inherently uncertain in nature. An important query for uncertain objects is the probabilistic nearest-neighbor query (PNN), which computes the probability of each object for being the nearest neighbor of a query point. Evaluating this query is computationally expensive, since it needs to consider the relationship among uncertain objects, and requires the use of numerical integration or Monte-Carlo methods. Sometimes, a query user may not be concerned about the exact probability values. For example, he may only need answers that have sufficiently high confidence. We thus propose the constrained nearest-neighbor query (C-PNN), which returns the IDs of objects whose probabilities are higher than some threshold, with a given error bound in the answers. The C-PNN can be answered efficiently with probabilistic verifiers. These are methods that derive the lower and upper bounds of answer probabilities, so that an object can be quickly decided on whether it should be included in the answer. We have developed three probabilistic verifiers, which can be used on uncertain data with arbitrary probability density functions. Extensive experiments were performed to examine the effectiveness of these approaches.