In this paper, we present algorithms and data structures for the top-k nearest neighbor searching where the input points are exact and the query point is uncertain under the L1 distance metric in the plane. The uncertain query point is represented by a discrete probability density function, and the goal is to return the top-k expected nearest neighbors, which have the smallest expected distances to the query point. Given a set of n exact points in the plane, we build an O(n log n log log n)-size data structure in O(n log n log log n) time, such that for any uncertain query point with m possible locations and any integer k with 1 k n, the top-k expected nearest neighbors can be found in O(mlogm + (k+m)log^2 n) time. Even for the special case where k = 1, our result is better than the previously best method (in PODS 2012), which requires O(n log^2 n) preprocessing time, O(n log^2 n) space, and O(m^2 log^3 n) query time. In addition, for the one-dimensional version of this problem, our approach can build an O(n)-size data structure in O(n log n) time that can support O(min mk,mlog m + k + log n) time queries and the query time can be reduced to O(k+m+log n) time if the locations of Q are given sorted. In fact, the problem is equivalent to the aggregate or group nearest neighbor searching with the weighted SUM as the aggregate distance function operator.
Data uncertainty is inherent in many applications, including sensor networks, scientific data management, data integration, locationbased applications, etc. One of common queries for uncertain data is the probabilistic nearest neighbor (PNN) query that returns all uncertain objects with non-zero probabilities to be NN. In this paper we study the PNN query with a probability threshold (PNNT), which returns all objects with the NN probability greater than the threshold. Our PNNT query removes the assumption in all previous papers that the probability of an uncertain object always adds up to 1, i.e., we consider missing probabilities. We propose an augmented R-tree index with additional probabilistic information to facilitate pruning as well as global data structures for maintaining the current pruning status. We present our algorithm for efficiently answering PNNT queries and perform experiments to show that our algorithm significantly reduces the number of objects that need to be further evaluated as NN candidates. This paper proposes a new problem, called superseding nearest neighbor search, on uncertain spatial databases, where each object is described by a multidimensional probability density function. Given a query point q, an object is a nearest neighbor (NN) candidate if it has a nonzero probability to be the NN of q. Given two NN-candidates o1 and o2, o1 supersedes o2 if o1 is more likely to be closer to q. An object is a superseding nearest neighbor (SNN) of q, if it supersedes all the other NN-candidates. Sometimes no object is able to supersede every other NN-candidate. In this case, we return the SNN-core-the minimum set of NN-candidates each of which supersedes all the NN-candidates outside the SNN-core. Intuitively, the SNN-core contains the best objects, because any object outside the SNN-core is worse than all the objects in the SNN-core. We show that the SNN-core can be efficiently computed by utilizing a conventional multidimensional index, as confirmed by extensive experiments. 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. The Voronoi diagram is an important technique for answering nearest-neighbor queries for spatial databases. In this paper, we study how the Voronoi diagram can be used on uncertain data, which are inherent in scientific and business applications. In particular, we propose the Uncertain-Voronoi Diagram (or UV-diagram in short). Conceptually, the data space is divided into distinct “UV-partitions”, where each UV-partition P is associated with a set S of objects; any point q located in P has the set S as its nearest neighbor with non-zero probabilities. The UV-diagram facilitates queries that inquire objects for having non-zero chances of being the nearest neighbor of a given query point. It also allows analysis of nearest neighbor information, e.g., finding out how many objects are the nearest neighbors in a given area. However, a UV-diagram requires exponential construction and storage costs. To tackle these problems, we devise an alternative representation for UV-partitions, and develop an adaptive index for the UV-diagram. This index can be constructed in polynomial time. We examine how it can be extended to support other related queries. We also perform extensive experiments to validate the effectiveness of our approach. Uncertainty pervades many domains in our lives. Current real-life applications, e.g., location tracking using GPS devices or cell phones, multimedia feature extraction, and sensor data management, deal with different kinds of uncertainty. Finding the nearest neighbor objects to a given query point is an important query type in these applications. In this paper, we study the problem of finding objects with the highest marginal probability of being the nearest neighbors to a query object. We adopt a general uncertainty model allowing for data and query uncertainty. Under this model, we define new query semantics, and provide several efficient evaluation algorithms. We analyze the cost factors involved in query evaluation, and present novel techniques to address the trade-offs among these factors. We give multiple extensions to our techniques including handling dependencies among data objects, and answering threshold queries. We conduct an extensive experimental study to evaluate our techniques on both real and synthetic data. 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. Nearest-neighbor queries are an important query type for commonly used feature databases. 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. A successful approach is to express the distance between two uncertain objects by probability density functions which assign a probability value to each possible distance value. By integrating the complete probabilistic distance function as a whole directly into the query algorithm, the full information provided by these functions is exploited. The result of such a probabilistic query algorithm consists of tuples containing the result object and a probability value indicating the likelihood that the object satisfies t he query predicate. In this paper we introduce an efficient strategy for cessing probabilistic nearest-neighbor queries, as the computation of these probability values is very expensive. In a detailed experimental evaluation, we demonstrate the benefits of our probabilistic query approach. The experiments show that we can achieve high quality query results with rather low computational cost. Nearest-neighbor (NN) search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for (i) computing all points that are nearest neighbors of a query point with nonzero probability; (ii) estimating, within a specified additive error, the probability of a point being the nearest neighbor of a query point; (iii) using it to return the point that maximizes the probability being the nearest neighbor, or all the points with probabilities greater than some threshold to be the NN. We also present some experimental results to demonstrate the effectiveness of our approach. The ability to store and query uncertain information is of great benefit to databases that infer values from a set of observations, including databases of moving objects, sensor readings, historical business transactions, and biomedical images. These observations are often inexact to begin with, and even if they are exact, a set of observations of an attribute of an object is better represented by a probability distribution than by a single number, such as a mean. In this paper, we present adaptive, piecewise-linear approximations (APLAs), which represent arbitrary probability distributions compactly with guaranteed quality. We also present the APLA-tree, an index structure for APLAs. Because APLA is more precise than existing approximation techniques, the APLA-tree can answer probabilistic range queries twice as fast. APLA generalizes to multiple dimensions, and the APLA-tree can index multivariate distributions using either one-dimensional or multidimensional APLAs. Finally, we propose a new definition of k-NN queries on uncertain data. The new definition allows APLA and the APLA-tree to answer k-NN queries quickly, even on arbitrary probability distributions. No efficient k-NN search was previously possible on such distributions.