# Skyline Diagram: Efficient Space Partitioning for Skyline Queries

## TL;DR

This paper introduces the Skyline Diagram, a novel space partitioning structure that efficiently facilitates skyline queries by dividing the plane into regions with identical skyline results, supported by algorithms and experimental validation.

## Contribution

It proposes the Skyline Diagram and algorithms for its construction, including an approximate version to reduce space, enhancing skyline query processing efficiency.

## Key findings

- Algorithms are efficient and scalable.
- The approximate skyline diagram reduces space costs.
- Experimental results validate effectiveness on real and synthetic data.

## Abstract

Skyline queries are important in many application domains. In this paper, we propose a novel structure Skyline Diagram, 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 $k^{th}$-order Voronoi diagram commonly used to facilitate $k$ nearest neighbor ($k$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.