Empty non-convex and convex four-gons in random point sets
نویسندگان
چکیده
Let S be a set of n points distributed uniformly and independently in a convex, bounded set in the plane. A four-gon is called empty if it contains no points of S in its interior. We show that the expected number of empty non-convex four-gons with vertices from S is 12n logn + o(n logn) and the expected number of empty convex four-gons with vertices from S is Θ(n). keywords: random point set, empty four-gon, polygon, geometric probability 2010 Mathematics Subject Classification. Primary 60D05, 52A22.
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تاریخ انتشار 2014