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AnO(n logn) plane-sweep algorithm forL 1 andL Delaunay triangulations

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Abstract

TheDelaunay diagram on a set of points in the plane, calledsites, is the straight-line dual graph of the Voronoi diagram. When no degeneracies are present, the Delaunay diagram is a triangulation of the sites, called theDelaunay triangulation. When degeneracies are present, edges must be added to the Delaunay diagram to obtain a Delaunay triangulation. In this paper we describe an optimalO(n logn) plane-sweep algorithm for computing a Delaunay triangulation on a possibly degenerate set of sites in the plane under theL 1 metric or theL metric.

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Communicated by Leonidas J. Guibas.

Supported by the National Science Foundation, through its Design, Tools and Test Program under Grant Number MIP 87-06139.

We are grateful to the two referees for their careful reading and helpful comments.

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Shute, G.M., Deneen, L.L. & Thomborson, C.D. AnO(n logn) plane-sweep algorithm forL 1 andL Delaunay triangulations. Algorithmica 6, 207–221 (1991). https://doi.org/10.1007/BF01759042

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  • DOI: https://doi.org/10.1007/BF01759042

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