Generating strictly binary trees at random based on convex polygon triangulations

Abstract

A set of maximal non-intersecting diagonals can decompose a polygon into triangles, and the edges and diagonals can be converted into the external and internal nodes of a strictly binary tree. This paper gives algorithms to generate all types of triangulations and triangulations at random. Based on that, this paper gives an algorithm to generate strictly binary trees at random. The experimental results show that the numbers of various shapes of strictly binary trees generated are nearly equal. The algorithm to generate strictly binary trees at random can be transformed to the algorithm to randomly generate binary trees.

Keywords:

• convex polygon triangulation
• edge
• diagonal
• strictly binary tree
• binary tree
• node
• recursive algorithm

2010 AMS Subject Classifications:

• 05C05
• 32B25
• 05C85

Acknowledgements

We are very grateful to the anonymous referees for their helpful comments and suggestions.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61075040].