# Generating triangulations at random

@article{Epstein1994GeneratingTA, title={Generating triangulations at random}, author={Peter Epstein and J{\"o}rg-R{\"u}diger Sack}, journal={ACM Trans. Model. Comput. Simul.}, year={1994}, volume={4}, pages={267-278} }

An <italic>O(n<supscrpt>3</supscrpt>)</italic> algorithm is described to count triangulations of a simple polygon with <italic>n</italic>vertices. This algorithm is used to construct an <italic>O(n<supscrpt>4</supscrpt>)</italic> algorithm to generate triangulations of a simple polygon at random with a uniform probability distribution. The problem of counting triangulations of a simple polygon is then related to existing problems in graph theory.

## 27 Citations

Randomly Generating Triangulations of a Simple Polygon

- Computer ScienceCOCOON
- 2005

An O(n^2 + |E|^{\frac{3}{2}}) time algorithm for generating triangulations of a simple polygon at random with uniform distribution, where n and |E | are the number of vertices and diagonal edges in the given polygon, respectively.

Graph of triangulations of a convex polygon and tree of triangulations

- Mathematics, Computer ScienceComput. Geom.
- 1999

Generating Random Polygons with Given Vertices

- Mathematics, Computer ScienceComput. Geom.
- 1996

An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation

- Computer Science, MathematicsSTACS
- 2003

We propose a new linear time algorithm to represent a planar graph. Based on a specific triangulation of the graph, our coding takes on average 5.03 bits per node, and 3.37 bits per node if the graph…

On typical triangulations of a convex $n$-gon

- MathematicsJournal of Combinatorics
- 2021

Let $f_n$ be a function assigning weight to each possible triangle whose vertices are chosen from vertices of a convex polygon $P_n$ of $n$ sides. Suppose ${\mathcal T}_n$ is a random triangulation,…

Random polygon generation using ‘GRP_AS’ heuristic

- Computer Science, Business2013 Sixth International Conference on Contemporary Computing (IC3)
- 2013

The proposed heuristic, “GRP_AS” is based on the principle of random selection of a line segment and angular sorting of the point set and takes O(nlogn) time which is less than that of “2-Opt Move” heuristic as well as ‘grP_CH’ heuristic.

Use of simple polygonal chains in generating random simple polygons

- Computer Science
- 2017

The experimental results show that the third algorithm produces more polygons rather than the well-known 2-opt move algorithm and the first algorithm acts better than the second algorithm, where both act better than steady Growth.

Exact uniform sampling over catalan structures

- Computer Science, MathematicsArXiv
- 2018

We present a new framework for creating elegant algorithms for exact uniform sampling of important Catalan structures, such as triangulations of convex polygons, Dyck words, monotonic lattice paths…

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