Amortized efficiency of generating planar paths in convex position

Authors:
Ro-Yu Wu;Jou-Ming Chang;Kung-Jui Pai;Yue-Li Wang
Affiliations:
Department of Industrial Management, Lunghwa University of Science and Technology, Taoyuan, Taiwan, ROC;Institute of Information and Decision Sciences, National Taipei College of Business, Taipei, Taiwan, ROC;Department of Industrial Engineering and Management, Mingchi University of Technology, Taipei, Taiwan, ROC;Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

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 1 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.