Generating strictly binary trees at random based on convex polygon triangulations. (English) Zbl 1338.05045
Summary: 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.
MSC:
| 05C05 | Trees |
| 32B25 | Triangulation and topological properties of semi-analytic and subanalytic sets, and related questions |
| 05C85 | Graph algorithms (graph-theoretic aspects) |
Keywords:
convex polygon triangulation; edge; diagonal; strictly binary tree; binary tree; node; recursive algorithmReferences:
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| [2] | DOI: 10.1007/978-3-662-04245-8 · doi:10.1007/978-3-662-04245-8 |
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