Expected size of random Tukey layers and convex layers

• Main Authors: Guo, Zhengyang, Li, Yi, Pei, Shaoyu
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Convex Layer; Tukey Depth
• Online Access: https://hdl.handle.net/10356/162710
• Institution: Nanyang Technological University

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 t...