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.