Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
Geometric tree graphs of points in convex position
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Lower bounds on the number of crossing-free subgraphs of KN
Computational Geometry: Theory and Applications
On local transformation of polygons with visibility properties
Theoretical Computer Science
Computational Geometry: Theory and Applications
On the diameter of geometric path graphs of points in convex position
Information Processing Letters
Amortized efficiency of generating planar paths in convex position
Theoretical Computer Science
| Hi-index | 0.89 |
We consider the problem of planar spanning tree transformation in a two-dimensional plane. Given two planar trees T"1 and T"2 drawn on a set S of n points in general position in the plane, the problem is to transform T"1 into T"2 by a sequence of simple changes called edge-flips or just flips. A flip is an operation by which one edge e of a geometric object is removed and an edge f (fe) is inserted such that the resulting object belongs to the same class as the original object. We present two algorithms for planar tree transformations. The first technique is an indirect approach which relies on some 'canonical' tree to obtain such transformation results. It is shown that it takes at most 2n-m-s-2 flips (m,s0) which is an improvement over the result in [D. Avis, K. Fukuda, Reverse search for enumeration, Discrete Applied Mathematics 65 (1996) 21-46]. Second, we present a direct approach which takes at most n-1+k flips (k=0) for such transformation when S in convex position and also show results when the points are in general position. We provide cases where the second technique performs an optimal number of flips. A counterexample is given to show that if |T"1@?T"2|=k then they cannot be transformed to one another by k flips.