Probabilistic Verifiers: Evaluating Constrained Nearest-Neighbor Queries over Uncertain Data

Abstract

Abstract-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.

UV-diagram: A Voronoi diagram for uncertain data

“…For simplicity, we use the numerical integration method of [14] to implement probability computation of answer objects. If faster methods such as [15] are used, the fraction of time spent on retrieving answer objects from the index will be higher, and thus it would be important to optimize the index (which is the focus of our work). All our programs were implemented in C++ and tested on a Core2 Duo 2.66GHz PC.…”

“…In [14], numerical integration techniques have been presented. Probabilistic verifiers, described in [15], can generate answer objects' probability bounds without performing expensive integration operations. Another way to compute answer probabilities is based on sampling [25].…”

“…Recently, researchers have proposed to consider uncertainty as a "first-class citizen" in a DBMS [15], [18]- [20]. Two models can be used to represent uncertain data: tuple-and attribute-uncertainty.…”

“…To evaluate PNN using the Rtree, a branch-and-prune strategy has been proposed in [14], where MBRs that may contain answer objects are traversed. However, this involves a lot of overhead in reading index nodes and leaf pages [14], [15]. Similar issues also occur with grids [16].However, retrieving answer objects from the UVdiagram is essentially a point query search: given a point q, find the objects associated with the UV-partition that contains q.…”

Threshold-based probabilistic top-k dominating queries

“…Uncertainty is inherent in such applications due to various factors such as data randomness and incompleteness, limitation of equipment, and delay or loss in data transfer. A number of issues have been recently addressed; these include modeling uncertainty [2,36], query evaluation [10,13,14,37], indexing [11,41], top-k queries [22,35,39,42], skyline queries [34], joins [26,27], nearest neighbor query [5,9,27], clustering [28,30], etc.…”