Peeling sequences: a directional method for the three-block construction

Abstract

A \emph{peeling sequence} of a finite planar point set is an ordering of point removals, in which each point is a vertex of the convex hull of the points not yet removed. Write $g(S)$ for the number of such sequences, and $g(n)$ for the minimum of $g(S)$ over $n$-point sets in general position. We present a method which can be used to prove better upper bounds on the previously analysed recursive 3-branch constructions $S_n$. In fact, we prove $g(n)\le g(S_n)=O(6.57^n)$, using directional restrictions and a weighted prefix-tree argument.

14 pages, 7 figures