Efficient computation of elliptic gabriel graph

Authors:
Changhee Lee;Donguk Kim;Hayong Shin;Deok-Soo Kim
Affiliations:
Dept. of Industrial Engineering, Hanyang University, Seoul, Korea;Dept. of Industrial Engineering, Hanyang University, Seoul, Korea;Dept. of Industrial Engineering, KAIST, Daejeon, Korea;Dept. of Industrial Engineering, Hanyang University, Seoul, Korea
Venue:
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Year:
2006

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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.