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|Title:||Expected size of random Tukey layers and convex layers||Authors:||Guo, Zhengyang
|Keywords:||Science::Mathematics||Issue Date:||2022||Source:||Guo, Z., Li, Y. & Pei, S. (2022). Expected size of random Tukey layers and convex layers. Computational Geometry, 103, 101856-. https://dx.doi.org/10.1016/j.comgeo.2021.101856||Journal:||Computational Geometry||Abstract:||We study the Tukey layers and convex layers of a planar point set, which consists of n points independently and uniformly sampled from a convex polygon with k vertices. We show that the expected number of vertices on the first t Tukey layers is O(ktlog(n/k)) and the expected number of vertices on the first t convex layers is O(kt3log(n/(kt2))). We also show a lower bound of Ω(tlogn) for both quantities in the special cases where k=3,4. The implications of those results in the average-case analysis of two computational geometry algorithms are then discussed.||URI:||https://hdl.handle.net/10356/162710||ISSN:||0925-7721||DOI:||10.1016/j.comgeo.2021.101856||Rights:||© 2021 Elsevier B.V. All rights reserved.||Fulltext Permission:||none||Fulltext Availability:||No Fulltext|
|Appears in Collections:||SPMS Journal Articles|
Updated on Dec 3, 2022
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