Efficient computation of elliptic Gabriel graph

Abstract

Searching neighboring points around a point in a point set has been important for various applications and there have been extensive studies such as the minimum spanning tree, relative neighborhood graph, Delaunay triangulation, Gabriel graph, and so on. Observing the fact that the previous approaches of neighbor search may possibly sample severely biased neighbors in a set of unevenly distributed points, an elliptic Gabriel graph has recently been proposed. By extending the influence region from a circle to an ellipse, the elliptic Gabriel graph generalizes the ordinary Gabriel graph. Hence, the skewness in the sampled neighbors is rather reduced. In this paper, we present a simple observation which allows to compute the correct elliptic Gabriel graph efficiently by reducing the search space.