A unified approach to ranking in probabilistic databases

Abstract

The dramatic growth in the number of application domains that naturally generate probabilistic, uncertain data has resulted in a need for efficiently supporting complex querying and decision-making over such data. In this paper, we present a unified approach to ranking and top-k query processing in probabilistic databases by viewing it as a multi-criteria optimization problem, and by deriving a set of features that capture the key properties of a probabilistic dataset that dictate the ranked result. We contend that a single, specific ranking function may not suffice for probabilistic databases, and we instead propose two parameterized ranking functions, called P RF ω and P RF e , that generalize or can approximate many of the previously proposed ranking functions. We present novel generating functions-based algorithms for efficiently ranking large datasets according to these ranking functions, even if the datasets exhibit complex correlations modeled using probabilistic and/xor trees or Markov networks. We further propose that the parameters of the ranking function be learned from user preferences, and we develop an approach to learn those parameters. Finally, we present a comprehensive experimental study that illustrates the effectiveness of our parameterized ranking functions, especially P RF e , at approximating other ranking functions and the scalability of our proposed algorithms for exact or approximate ranking.

Top (<i>k</i>₁,<i>k</i>₂) Query in Uncertain Datasets

“…Tuples in L are processed one by one in the second for loop to calculate P k 1 (t j ) and update P k 1 …”

“…Some x-tuples with negligible P k 1 probabilities can be pruned early. In this section, we estimate an upper bound of P k 1 …”

“…At the same time, uncertainty is inherent in many datasets due to various factors like noise [1], privacy protection strategy [2], incompleteness of data and delay or loss in data transfer [3]. In this paper, we connect top k query and uncertain data model, and propose a novel top (k 1 , k 2 ) query in uncertain datasets.…”

“…Sum of these instances' probabilities is no more than 1. For example in Table 1, t 11 and t 12 are two tuples of x-tuple T 1 . t 11 and t 12 cannot appear at the same time.…”

Continuous Probabilistic Sum Queries in Wireless Sensor Networks with Ranges

“…It is well known that the multiplication of two polynomials of degree O(n) can be done in O(n log n) time using FFT. Furthermore, the approach by [19], using divide-and-conquer and Fast Fourier Transformation allows us to further reduce this time complexity to O(n log 2 n). Unless s dir is the root, s dir uses Corollaries 1 and 2 to reduce the size of its polynomial, and sends the resulting polynomial to its parent node.…”