2023/02/08 by Travis Dillon, Dillon, Travis, Narmada Varadarajan +1 · 1 citation
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2302.04244
openalex publication_date 2023/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The number of steps required to exhaust a point set by iteratively removing the vertices of its convex hull is called the layer number of the point set. This article presents a short proof that the layer number of the grid \1,2,…,n\d is at most (1)/(4)dn2+1, significantly improving the dependence on d in the best-known upper bound. We also prove a lower bound of (1)/(2)d(n-1)+1, which shows that the layer number of the grid is linear in d.