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- W3212295152 abstract "In this paper, we study the problem of counting the number of convex empty polygons in a given set of n points in general position in the plane. We present two algorithms: one counts the number of all convex empty polygons in O(T) time and the other counts the number of convex empty m-gons for all 3≤m≤k in O(kT) time, where T denotes the number of empty triangles in S. Note that T varies from Ω(n2) to O(n3), while its expected value is known to be Θ(n2) when n input points are chosen uniformly and independently at random from a convex and bounded body." @default.
- W3212295152 created "2021-11-22" @default.
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- W3212295152 date "2022-04-01" @default.
- W3212295152 modified "2023-09-27" @default.
- W3212295152 title "Faster counting empty convex polygons in a planar point set" @default.
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- W3212295152 doi "https://doi.org/10.1016/j.ipl.2021.106221" @default.
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