Common Edges in Rooted Trees and Polygonal Triangulations

Author:

Cleary Sean,Rechnitzer Andrew,Wong Thomas

Abstract

Rotation distance between rooted binary trees measures the degree of similarity of two trees with ordered leaves and is equivalent to edge-flip distance between triangular subdivisions of regular polygons. There are no known polynomial-time algorithms for computing rotation distance. Existence of common edges makes computing rotation distance more manageable by breaking the problem into smaller subproblems. Here we describe the distribution of common edges between randomly-selected triangulations and measure the sizes of the remaining pieces into which the common edges separate the polygons. We find that asymptotically there is a large component remaining after sectioning off numerous small polygons which gives some insight into the distribution of such distances and the difficulty of such distance computations, and we analyze the distributions of the sizes of the largest and smaller resulting polygons.

Publisher

The Electronic Journal of Combinatorics

Subject

Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An Efficient Sampling Algorithm for Difficult Tree Pairs;Acta Cybernetica;2022-01-21

2. Edge Conflicts do not Determine Geodesics in the Associahedron;SIAM Journal on Discrete Mathematics;2018-01

3. Expected maximum vertex valence in pairs of polygonal triangulations;Involve, a Journal of Mathematics;2015-09-28

4. Average reductions between random tree pairs;Involve, a Journal of Mathematics;2015-01-01

5. Expected conflicts in pairs of rooted binary trees;Involve, a Journal of Mathematics;2013-09-08

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