Computing the kernel of a point set in a polygon
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ElGindy posed the following problem: given a simple polygon P of n vertices and a set S of k points inside P, find the collection of points of P that can see all points of S. This collection of points is called the kernel of S in P. In this paper, we study this problem and show that the kernel of S can be computed in O(n log log n+k log n+k log k) time and O(n+k) space. We also present an O(n log n+k log k) time and O(n+k) space algorithm to determine if there exists a line segment in P that can see all points of S, and if so, to find the shortest one. Several other related problems are also addressed.
KeywordsConvex Hull Convex Polygon Simple Polygon Geodesic Path Prefer Side
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