A Linear Algorithm for Finding the Convex Hull of a Simple Polygon

The problem of determining the convex hull of a set of n points in the plane has recently received a good deal of attention. Several algorithms for the general problem with worst case complexity D(n log n) have appeared (e.g., [3,4,6]). The special case where the points form the vertices of a simple polygon has long been considered easier. Indeed, Sklansky [S] has proposed an O(n) algorithm, but a. recently published counter example of Bykat [2] shows that the algorithm can sometimes fail. A slightly different counterexample can be constructed for a similar algorithm of Shamos [4]. In this note we present and prove the validity of a new linear time algorithm for this problem.