Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon

Eunjin Oh; Hee-Kap Ahn

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arXiv · 1801.02292

Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon

Eunjin Oh·Hee-Kap Ahn

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Abstract

Given a set of sites in a simple polygon, a geodesic Voronoi diagram of the sites partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones for m <= n/ polylog n. Moreover, the algorithms for the geodesic nearest-point and farthest-point Voronoi diagrams are optimal for m <= n/ polylog n. This partially answers a question posed by Mitchell in the Handbook of Computational Geometry.

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BibTeX RIS

Eunjin Oh, Hee-Kap Ahn. 2018-01-08. Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon. https://arxiv.org/abs/1801.02292

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