Efficiently Producing the K Nearest Neighbors in the Skyline on Vertically Partitioned Tables

Abstract

Criteria that induce a Skyline naturally represent user's preference conditions useful to discard irrelevant data in large datasets. However, in the presence of high-dimensional Skyline spaces, the size of the Skyline can still be very large, making unfeasible for users to process this set of points. To identify the best points among the Skyline, the Top-k Skyline approach has been proposed. Top-k Skyline uses discriminatory criteria to induce a total order of the points that comprise the Skyline, and recognizes the best or top-k points based on these criteria. In this article the authors model queries as multi-dimensional points that represent bounds of VPT (Vertically Partitioned Table) property values, and datasets as sets of multi-dimensional points; the problem is to locate the k best tuples in the dataset whose distance to the query is minimized. A tuple is among the k best tuples whenever there is not another tuple that is better in all dimensions, and that is closer to the query point, i.e., the k best tuples correspond to the k nearest points to the query that are incomparable or belong to the skyline. The authors name these tuples the k nearest neighbors in the skyline. The authors propose a hybrid approach that combines Skyline and Top-k solutions and develop two algorithms: TKSI and k-NNSkyline. The proposed algorithms identify among the skyline tuples, the k ones with the lowest values of the distance metric, i.e., the k nearest neighbors to the multi-dimensional query that are incomparable. Empirically, we study the performance and quality of TKSI and k-NNSkyline. The authors’ experimental results show the TKSI is able to speed up the computation of the Top-k Skyline in at least 50% percent with respect to the state-of-the-art solutions, whenever k is smaller than the size of the Skyline. Additionally, the authors’ results suggest that k-NNSkyline outperforms existing solutions by up to three orders of magnitude.