The Largest Empty Circle Problem
نویسنده
چکیده
The largest empty circle (LEC) problem is defined on a set P and consists of finding the largest circle that contains no points in P and is also centered inside the convex hull of P . The LEC is always centered at either a vertex on the Voronoi diagram for P or on an intersection between a Voronoi edge and the convex hull of P . Thus, finding the LEC consists of constructing a Voronoi diagram and convex hull for P , then searching the Voronoi vertices and intersections between Voronoi edges and convex hull edges to see where the LEC lies. This paper presents a simpleO(n[h+ log n]) solution to the largest empty circle problem. Though previous work on this problem has found O(n log n) solutions, we find that for data sets which are somewhat normally distributed, h is small and our simple algorithm performs well.
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