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# Constrained Geodesic Centers of a Simple Polygon

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LIPIcs.SWAT.2016.29.pdf
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## Cite As

Eunjin Oh, Wanbin Son, and Hee-Kap Ahn. Constrained Geodesic Centers of a Simple Polygon. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.SWAT.2016.29

## Abstract

For any two points in a simple polygon P, the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regions. In this paper, we show how to compute the geodesic centers constrained to a set of line segments or simple polygonal regions contained in P. Our results provide substantial improvements over previous algorithms.
##### Keywords
• Geodesic distance
• simple polygons
• constrained center
• facility location
• farthest-point Voronoi diagram

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## References

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