Uniform random generations and rejection method(I) with binomial majorant

TL;DR

This paper introduces three efficient algorithms for uniformly generating Fibonacci words, Schr{"o}der trees, and Motzkin left factors, with an average complexity of O(n) in the RAM model.

Contribution

The paper presents new simple algorithms for uniform generation of specific combinatorial structures with optimal average complexity.

Findings

Algorithms operate in O(n) average time

Applicable to Fibonacci words, Schr{"o}der trees, and Motzkin factors

Efficient uniform sampling method

Abstract

We present three simple algorithms to uniformly generate `Fibonacci words' (i.e., some words that are enumerated by Fibonacci numbers), Schr{\"o}der trees of size $n$ and Motzkin left factors of size $n$ and final height $h$. These algorithms have an average complexity of $O(n)$ in the unit-cost RAM model.