Some Computational Aspects of Geodesic Convex Sets in a Simple Polygon |
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| Authors: | P T An D T Giang N N N Hai |
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| Institution: | 1. CEMAT, Instituto Superior Técnico , Lisboa, Portugal;2. Institute of Mathematics , Hanoi, Vietnam thanhan@math.ist.utl.pt;4. Department of Mathematics , Vinh University , Vinh, Vietnam;5. Department of Mathematics , International University , Ho Chi Minh City, Vietnam |
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| Abstract: | In this article, we deal with some computational aspects of geodesic convex sets. Motzkin-type theorem, Radon-type theorem, and Helly-type theorem for geodesic convex sets are shown. In particular, given a finite collection of geodesic convex sets in a simple polygon and an “oracle,” which accepts as input three sets of the collection and which gives as its output an intersection point or reports its nonexistence; we present an algorithm for finding an intersection point of this collection. |
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| Keywords: | Euclidean geodesic path Geodesic convex set Geodesic convex hull Helly's theorem Radon's theorem |
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