Exact enumeration of self-avoiding walks

TL;DR

This paper advances enumeration techniques for self-avoiding walks, enabling enumeration up to 36 steps on a cubic lattice, significantly improving speed and efficiency.

Contribution

The paper introduces a new methodology that drastically accelerates the exact enumeration process for self-avoiding walks.

Findings

Enumeration of walks up to 36 steps on cubic lattice achieved

Enumeration process is thousands to millions times faster

Methodology improves testing and comparison of enumeration techniques

Abstract

A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of times faster. This allowed us to enumerate self-avoiding walks on the simple cubic lattice up to a length of 36 steps.