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On 2-Site Voronoi Diagrams Under Geometric Distance Functions

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Abstract

We revisit a new type of Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, namely, circles and triangles, and analyze the structure and complexity of the nearest- and furthest-neighbor 2-site Voronoi diagrams of a point set in the plane with respect to these distance functions. In addition, we bring to notice that 2-point site Voronoi diagrams can be alternatively interpreted as 1-site Voronoi diagrams of segments, and thus, our results also enhance the knowledge on the latter.

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Correspondence to Gill Barequet.

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David Eppstein was supported by National Science Foundation of USA under Grants Nos. 0830403 and 1217322 and US Office of Naval Research under Grant No. N00014-08-1-1015.

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Barequet, G., Dickerson, M., Eppstein, D. et al. On 2-Site Voronoi Diagrams Under Geometric Distance Functions. J. Comput. Sci. Technol. 28, 267–277 (2013). https://doi.org/10.1007/s11390-013-1328-2

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  • DOI: https://doi.org/10.1007/s11390-013-1328-2

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