On Planar Path Transformation

A flip or edge-replacement is considered as a transformation by which one edge e of a geometric object is removed and an edge f (f = e) is inserted such that the resulting object belongs to the same class as the original object. In this paper, we consider Hamiltonian planar paths as geometric objects. A technique is presented for transforming a given planar path into another one for a set S of n points in convex position in the plane. Under these conditions, we show that any planar path can be transformed into another planar path by at most 2n - 5 flips. For the case when the points are in general position we provide experimental results regarding transformability of any planar path into another. We show that for n 8 points in general position any two paths can be transformed into each other. For n points in convex position we show that there are n2n-2 directed Hamiltonian planar paths. An algorithm is presented which uses flips of size 1 and flips of size 2 to generate all such path...

• Type: Conference
• Year: 2006
• Where: CCCG
• Authors: Kamrul Islam, Selim G. Akl, Henk Meijer
• Keywords: CCCG 2006, CCCG 2007, Geometric Objects, Hamiltonian Planar Paths, Planar Paths