A variant of the Recoil Growth algorithm to generate multi-polymer systems

TL;DR

This paper introduces a modified Recoil Growth algorithm that constrains polymer generation on specific graph classes, balancing computational efficiency and success rate, with a theoretical proof of its irreducibility.

Contribution

It proposes a new variant of the Recoil Growth algorithm with graph constraints and provides a theoretical irreducibility bound applicable to both the new and original algorithms.

Findings

The constrained algorithm improves computational efficiency.

A lower bound on irreducibility is established.

The method maintains sampling effectiveness.

Abstract

The Recoil Growth algorithm, proposed in 1999 by Consta et al., is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding paths. In this paper, we study a variant of the original Recoil Growth algorithm, where we constrain the generation of a new polymer to take place on a specific class of graphs. This makes it possible to make a fine trade-off between computational cost and success rate. We moreover give a simple proof for a lower bound on the irreducibility of this new algorithm, which applies to the original algorithm as well.