Enumeration of Hamiltonian walks in two and three dimensional lattices

TL;DR

This paper introduces an efficient centroid-based method implemented in Java for exactly enumerating Hamiltonian walks in large 2D and 3D lattices, aiding protein design and polymer analysis.

Contribution

It presents a novel, efficient enumeration technique for Hamiltonian walks in large lattices using centroids, with practical applications in biophysics.

Findings

Exact enumeration of Hamiltonian walks in large lattices achieved

Method applicable to square and simple cubic lattices

Potential applications in protein sequence design and polymer structure analysis

Abstract

We report an efficient methodology for enumerating the Hamiltonian walks in two and three dimensional lattices of large sizes, using the concept of centroids. This strategy, with the help of JAVA programming enables the exact computation of the Hamiltonian walks for square and simple cubic lattices. These estimates are useful in designing the protein sequences using hydrophobic-polar lattice models as well as in the analysis of secondary structures in compact polymers.