Abstract

This paper contains a simple, randomized algorithm for constructing the convex hull of a set of n points in the plane with expected running time O(n log h) where h is the number of points on the convex hull. Introduction Determining the convex hull of a set of points is one of the most basic problems in computational geometry. Ron Graham presented the first O(n log n) algorithm for finding the convex hull of points in the plane in 1972 [12]. The following year, R. Jarvis gave an algorithm whose running time depends on the output size [14]. Jarvis's algorithm runs in O(nh) time where h is the number of points in the convex hull. The next ten years saw many other algorithms for finding convex hulls in the plane most of which run in O(n log n) time [1, 4, 11, 13, 16]. Some very simple algorithms were proposed which have O(n) expected running time for many distributions of points in the plane (such as points with normal density) [10, 3]. During this period, Avis [2] and Yao [20] proved...

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