Constructing the convex hull of a partially sorted set of points

Abstract

In this paper we give an optimal algorithm for constructing the convex hull of a partially sorted set S of n points in R 2. Specifically, we assume S is represented as the union of a collection of non-empty subsets S 0, S 1, S 2,…, S m , where the x-coordinate of each point in S i is smaller than the x-coordinate of any point in S j if i < j. Our method runs in O( n log h max) time, where h max is the maximum number of hull edges incident on the points of any single subset S i . In fact, if one is only interested in finding the hull edges that ‘bridge’ different subsets, then our method runs in O( n) time.