K-Dominance in Multidimensional Data: Theory and Applications

We study the problem of k-dominance in a set of d-dimensional vectors, prove bounds on the number of maxima (skyline vectors), under both worst-case and average-case models, perform experimental evaluation using synthetic and real-world data, and explore an application of k-dominant skyline for extracting a small set of top-ranked vectors in high dimensions where the full skylines can be unmanageably large

Missing values estimation for skylines in incomplete database

Incompleteness of data is a common problem in many databases including web heterogeneous databases, multi-relational databases, spatial and temporal databases and data integration. The incompleteness of data introduces challenges in processing queries as providing accurate results that best meet the query conditions over incomplete database is not a trivial task. Several techniques have been proposed to process queries in incomplete database. Some of these techniques retrieve the query results based on the existing values rather than estimating the missing values. Such techniques are undesirable in many cases as the dimensions with missing values might be the important dimensions of the user’s query. Besides, the output is incomplete and might not satisfy the user preferences. In this paper we propose an approach that estimates missing values in skylines to guide users in selecting the most appropriate skylines from the several candidate skylines. The approach utilizes the concept of mining attribute correlations to generate an Approximate Functional Dependencies (AFDs) that captured the relationships between the dimensions. Besides, identifying the strength of probability correlations to estimate the values. Then, the skylines with estimated values are ranked. By doing so, we ensure that the retrieved skylines are in the order of their estimated precision

RRR: Rank-Regret Representative

Selecting the best items in a dataset is a common task in data exploration. However, the concept of "best" lies in the eyes of the beholder: different users may consider different attributes more important, and hence arrive at different rankings. Nevertheless, one can remove "dominated" items and create a "representative" subset of the data set, comprising the "best items" in it. A Pareto-optimal representative is guaranteed to contain the best item of each possible ranking, but it can be almost as big as the full data. Representative can be found if we relax the requirement to include the best item for every possible user, and instead just limit the users' "regret". Existing work defines regret as the loss in score by limiting consideration to the representative instead of the full data set, for any chosen ranking function. However, the score is often not a meaningful number and users may not understand its absolute value. Sometimes small ranges in score can include large fractions of the data set. In contrast, users do understand the notion of rank ordering. Therefore, alternatively, we consider the position of the items in the ranked list for defining the regret and propose the {\em rank-regret representative} as the minimal subset of the data containing at least one of the top-$k$ of any possible ranking function. This problem is NP-complete. We use the geometric interpretation of items to bound their ranks on ranges of functions and to utilize combinatorial geometry notions for developing effective and efficient approximation algorithms for the problem. Experiments on real datasets demonstrate that we can efficiently find small subsets with small rank-regrets

Probabilistic Skyline Queries over Uncertain Moving Objects

Data uncertainty inherently exists in a large number of applications due to factors such as limitations of measuring equipments, update delay, and network bandwidth. Recently, modeling and querying uncertain data have attracted considerable attention from the database community. However, how to perform advanced analysis on uncertain data remains an interesting question. In this paper, we focus on the execution of skyline computation over uncertain moving objects. We propose a novel probabilistic skyline model where an uncertain object may take a probability to be in the skyline at a certain time point, therefore a p-t-skyline contains those moving objects whose skyline probabilities are at least p at time point t. Computing probabilistic skyline over a large number of uncertain moving objects is a daunting task in practice. In order to efficiently compute the probabilistic skyline query, we propose a discrete-and-conquer strategy, which follows the sampling-bounding-pruning-refining procedure. To further reduce the skyline computation cost, we propose an enhanced framework that is based on a multi-dimensional indexing structure combined with the discrete-and-conquer strategy. Through extensive experiments with synthetic datasets, we show that the framework can efficiently support skyline queries over uncertain moving object and is scalable on large data sets

Skyline queries over incomplete multidimensional database

In recent years, there has been much focus on skyline queries that incorporate and provide more flexible query operators that return data items which are dominating other data items in all attributes (dimensions).Several techniques for skyline have been proposed in the literature.Most of the existing skyline techniques aimed to find the skyline query results by supposing that the values of dimensions are always present for every data item.In this paper we aim to evaluate the skyline preference queries in which some dimension values are missing.We proposed an approach for answering preference queries in a database by utilizing the concept of skyline technique.The skyline set selected for a given query operation is then optimized so that the missing values are replaced with some approximate values that provide a skyline answer with complete data.This will significantly reduce the number of comparisons between data items.Beside that, the number of retrieved skyline data items is reduced and this guides the users to select the most appropriate data items from the several alternative complete skyline data items