Computation of Spatial Skyline Points

TL;DR

This paper presents an efficient method for computing spatial skyline points by reducing the problem to a weighted Voronoi diagram, enabling an $O((n + m) ext{log}(n + m))$ algorithm in 2D.

Contribution

It introduces a novel reduction of the skyline computation to weighted Voronoi diagram construction under convex distance functions, improving computational efficiency.

Findings

Provides an $O((n + m) ext{log}(n + m))$ algorithm for 2D cases.

Reduces skyline computation to Voronoi diagram analysis.

Applicable to spatial data analysis and location-based services.

Abstract

We discuss a method of finding skyline or non-dominated sites in a set $P$ of $n$ point sites with respect to a set $S$ of $m$ points. A site $p \in P$ is non-dominated if and only if for each $q \in P \setminus \{p\}$, there exists at least one point $s \in S$ that is closer to $p$ than to $q$. We reduce this problem of determining non-dominated sites to the problem of finding sites that have non-empty cells in an additively weighted Voronoi diagram under a convex distance function. The weights of said Voronoi diagram are derived from the coordinates of the sites of $P$, while the convex distance function is derived from $S$. In the two-dimensional plane, this reduction gives an $O((n + m) \log (n + m))$-time algorithm to find the non-dominated points.