Amortized efficiency of generating planar paths in convex position
Let S be a set of n >= 3 points arranged in convex position in the plane and suppose that all points of S are labeled from I to n in clockwise direction. A planar path P on S is a path whose edges connect all points of S with straight line segments such that no two edges of P cross. Flipping an edge on P means that a new path P' is obtained from P by a single edge replacement. In this paper, we provide efficient algorithms to generate all planar paths. With the help of a loopless algorithm to produce a set of 2-way binary-reflected Gray codes, the proposed algorithms generate the next planar path by means of a flip and such that the number of position changes for points in the path has a constant amortized upper bound. (C) 2011 Elsevier B.V. All rights reserved.
planar paths convex position gray codes amortized analysis enumeration algorithms geometric graphs