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Some Computational Aspects of Geodesic Convex Sets in a Simple Polygon

An, P. T. ; Giang, D. T.; Hai, N. N. N.

Numerical Functional Analysis and Optimization, 31(3) (2010), 221-231

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.