Group-Based Skyline for Pareto Optimal Groups

Abstract

Skyline computation, aiming at identifying a set of skyline points that are not dominated by any other point, is particularly useful for multi-criteria data analysis and decision making. Traditional skyline computation, however, is inadequate to answer queries that need to analyze not only <italic>individual</italic> points but also <italic>groups</italic> of points. To address this gap, we generalize the original skyline definition to the novel group-based skyline (G-Skyline), which represents Pareto optimal groups that are not dominated by other groups. In order to compute G-Skyline groups consisting of <inline-formula><tex-math notation= LaTeX >$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href= liu-ieq1-2960347.gif /></alternatives></inline-formula> points efficiently, we present a novel structure that represents the points in a directed skyline graph and captures the dominance relationships among the points based on the first <inline-formula><tex-math notation= LaTeX >$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href= liu-ieq2-2960347.gif /></alternatives></inline-formula> skyline layers. We propose efficient algorithms to compute the first <inline-formula><tex-math notation= LaTeX >$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href= liu-ieq3-2960347.gif /></alternatives></inline-formula> skyline layers. We then present two heuristic algorithms to efficiently compute the G-Skyline groups: the point-wise algorithm and the unit group-wise algorithm, using various pruning strategies. We observe that the number of G-Skyline groups of a dataset can be significantly large, we further propose the top-<inline-formula><tex-math notation= LaTeX >$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href= liu-ieq4-2960347.gif /></alternatives></inline-formula> representative G-Skyline groups based on the number of dominated points and the number of dominated groups and present efficient algorithms for computing them. The experimental results on the real NBA dataset and the synthetic datasets show that G-Skyline is interesting and useful, and our algorithms are efficient and scalable.