Skyline Diagram: Efficient Space Partitioning for Skyline Queries

Skyline queries are important in many application domains. In this paper, we propose a novel structure <italic>Skyline Diagram</italic>, which given a set of points, partitions the plane into a set of regions, referred to as skyline polyominos. All query points in the same skyline polyomino have the same skyline query results. Similar to <italic><inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="liu-ieq1-2923914.gif"/></alternatives></inline-formula>th-order Voronoi diagram</italic> commonly used to facilitate <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="liu-ieq2-2923914.gif"/></alternatives></inline-formula> nearest neighbor (<inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="liu-ieq3-2923914.gif"/></alternatives></inline-formula>NN) queries, skyline diagram can be used to facilitate skyline queries and many other applications. However, it may be computationally expensive to build the skyline diagram. By exploiting some interesting properties of skyline, we present several efficient algorithms for building the diagram with respect to three kinds of skyline queries, quadrant, global, and dynamic skylines. In addition, we propose an approximate skyline diagram which can significantly reduce the space cost. Experimental results on both real and synthetic datasets show that our algorithms are efficient and scalable.

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