Random $k$-noncrossing RNA Structures

TL;DR

This paper presents polynomial-time algorithms for uniformly generating random $k$-noncrossing matchings and RNA structures, leveraging combinatorial bijections and stochastic process modeling.

Contribution

It introduces a novel approach combining bijections and stochastic processes to efficiently generate random $k$-noncrossing structures with uniform probability.

Findings

Algorithms run in polynomial time.

Uniform sampling of $k$-noncrossing structures achieved.

Utilizes bijection with oscillating tableaux and stochastic paths.

Abstract

In this paper we derive polynomial time algorithms that generate random $k$-noncrossing matchings and $k$-noncrossing RNA structures with uniform probability. Our approach employs the bijection between $k$-noncrossing matchings and oscillating tableaux and the $P$-recursiveness of the cardinalities of $k$-noncrossing matchings. The main idea is to consider the tableaux sequences as paths of stochastic processes over shapes and to derive their transition probabilities.