Skyline computation is widely used in multicriteria decision making. As research in uncertain databases draws increasing attention, skyline queries with uncertain data have also been studied. Some earlier work focused on probabilistic skylines with a given threshold; Atallah and Qi [2009] studied the problem to compute skyline probabilities for all instances of uncertain objects without the use of thresholds, and proposed an algorithm with subquadratic time complexity. In this work, we propose a new algorithm for computing all skyline probabilities that is asymptotically faster: worst-case O(n √ n log n ) time and O(n) space for 2D data; O ( n 2−1/d log d −1 n ) time and O(n log d −2 n ) space for d -dimensional data. Furthermore, we study the online version of the problem: Given any query point p (unknown until the query time), return the probability that no instance in the given data set dominates p . We propose an algorithm for answering such an online query for d -dimensional data in O(n 1−1/ d log d −1 n ) time after preprocessing the data in O(n 2−1/d log d −1 ) time and space.

The probabilistic threshold query (PTQ) is one of the most common queries in uncertain databases, where all results satisfying the query with probabilities that meet the threshold requirement are returned. PTQ is used widely in nearest-neighbor queries, range queries, ranking queries, etc. In this paper, we investigate the general PTQ for arbitrary SQL queries that involve selections, projections and joins. The uncertain database model that we use is one that combines both attribute and tuple uncertainty as well as correlations between arbitrary attribute sets. We address the PTQ optimization problem that aims at improving the efficiency of PTQ query execution by enabling alternative query plan enumeration for optimization. We propose general optimization rules as well as rules specifically for selections, projections and joins. We introduce a threshold operator (τ-operator) to the query plan and show it is generally desirable to push down the τ-operator as much as possible.

Skyline computation is widely used in multi-criteria decision making. As research in uncertain databases draws increasing attention, skyline queries with uncertain data have also been studied, e.g. probabilistic skylines. The previous work requires "thresholding" for its efficiency -- the efficiency relies on the assumption that points with skyline probabilities below a certain threshold can be ignored. But there are situations where "thresholding" is not desirable -- low probability events cannot be ignored when their consequences are significant. In such cases it is necessary to compute skyline probabilities of all data items. We provide the first algorithm for this problem whose worst-case time complexity is sub-quadratic. The techniques we use are interesting in their own right, as they rely on a space partitioning technique combined with using the existing dominance counting algorithm. The effectiveness of our algorithm is experimentally verified.

We give efficient protocols for secure and private k-nearest neighbor (k-NN) search, when the data is distributed between two parties who want to cooperatively compute the answers without revealing to each other their private data. Our protocol for the single-step k-NN search is provably secure and has linear computation and communication complexity. Previous work on this problem had a quadratic complexity, and also leaked information about the parties' inputs. We adapt our techniquesto also solve the general multi-step k-NN search, and describe a specific embodiment of it for the case of sequence data. The protocols and correctness proofs can be extended to suit other privacy-preserving data mining tasks, such as classification and outlier detection.