Amortized efficiency of generating planar paths in convex position

• Published in: Theoretical computer science Vol. 412; no. 35; pp. 4504 - 4512
• Main Authors: Wu, Ro-Yu, Chang, Jou-Ming, Pai, Kung-Jui, Wang, Yue-Li
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 12.08.2011; Elsevier
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Amortized analysis; Applied sciences; Binary codes; Computer science; control theory; systems; Convex position; Enumeration algorithms; Exact sciences and technology; Geometric graphs; Gray codes; Information retrieval. Graph; Miscellaneous; Planar paths; Planes; Segments; Straight lines; Theoretical computing; Upper bounds; Enumeration algorithms; Gray codes; Convex position; Geometric graphs; Amortized analysis; Planar paths; Gray code; Enumeration; Computer theory; Line segment; Label; Replacement; Algorithm; Binary code; Upper bound; Efficiency
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2011.04.017

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.