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.
Uncertain relational models have been studied since the early 90's, and the first works on this topic mainly focused on theoretical aspects of probabilistic and possibilistic data management @cite_25 @cite_12 @cite_19 @cite_0 @cite_2 @cite_11 @cite_14 . More recently, there have been successful initiatives to build working systems for the efficient execution of queries over uncertain data @cite_5 @cite_27 @cite_18 @cite_23 @cite_13 @cite_16 @cite_1 .
@cite_18 @cite_14 @cite_1 @cite_0 @cite_19 @cite_27 @cite_23 @cite_2 @cite_5 @cite_16 @cite_13 @cite_25 @cite_12 @cite_11
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Several real-world applications need to effectively manage and reason about large amounts of data that are inherently uncertain. For instance, pervasive computing applications must constantly reason about volumes of noisy sensory readings for a variety of reasons, including motion prediction and human behavior modeling. Such probabilistic data analyses require sophisticated machine-learning tools that can effectively model the complex spatio temporal correlation patterns present in uncertain sensory data. Unfortunately, to date, most existing approaches to probabilistic database systems have relied on somewhat simplistic models of uncertainty that can be easily mapped onto existing relational architectures: Probabilistic information is typically associated with individual data tuples, with only limited or no support for effectively capturing and reasoning about complex data correlations. In this paper, we introduce BayesStore, a novel probabilistic data management architecture built on the principle of handling statistical models and probabilistic inference tools as first-class citizens of the database system. Adopting a machine-learning view, BAYESSTORE employs concise statistical relational models to effectively encode the correlation patterns between uncertain data, and promotes probabilistic inference and statistical model manipulation as part of the standard DBMS operator repertoire to support efficient and sound query processing. We present BAYESSTORE's uncertainty model based on a novel, first-order statistical model, and we redefine traditional query processing operators, to manipulate the data and the probabilistic models of the database in an efficient manner. Finally, we validate our approach, by demonstrating the value of exploiting data correlations during query processing, and by evaluating a number of optimizations which significantly accelerate query processing. Although the relational model for databases provides a great range of advantages over other data models, it lacks a comprehensive way to handle incomplete and uncertain data. Uncertainty in data values, however, is pervasive in all real-world environments and has received much attention in the literature. Several methods have been proposed for incorporating uncertain data into relational databases. However, the current approaches have many shortcomings and have not established an acceptable extension of the relational model. In this paper, we propose a consistent extension of the relational model. We present a revised relational structure and extend the relational algebra. The extended algebra is shown to be closed, a consistent extension of the conventional relational algebra, and reducible to the latter. This paper explores an inherent tension in modeling and querying uncertain data: simple, intuitive representations of uncertain data capture many application requirements, but these representations are generally incomplete―standard operations over the data may result in unrepresentable types of uncertainty. Complete models are theoretically attractive, but they can be nonintuitive and more complex than necessary for many applications. To address this tension, we propose a two-layer approach to managing uncertain data: an underlying logical model that is complete, and one or more working models that are easier to understand, visualize, and query, but may lose some information. We explore the space of incomplete working models, place several of them in a strict hierarchy based on expressive power, and study their closure properties. We describe how the two-layer approach is being used in our prototype DBMS for uncertain data, and we identify a number of interesting open problems to fully realize the approach. We investigate the impact of uncertainty on relational data -base schema design. Uncertainty is modeled qualitatively by assigning to tuples a degree of possibility with which they occur, and assigning to functional dependencies a degree of certainty which says to which tuples they apply. A design theory is developed for possibilistic functional dependencies, including efficient axiomatic and algorithmic characterizations of their implication problem. Naturally, the possibility degrees of tuples result in a scale of different degrees of data redundancy. Scaled versions of the classical syntactic Boyce-Codd and Third Normal Forms are established and semantically justified in terms of avoiding data redundancy of different degrees. Classical decomposition and synthesis techniques are scaled as well. Therefore, possibilistic functional dependencies do not just enable designers to control the levels of data integrity and losslessness targeted but also to balance the classical trade-off between query and update efficiency. Extensive experiments confirm the efficiency of our framework and provide original insight into relational schema design.