SAWdoubler: a program for counting self-avoiding walks

TL;DR

SAWdoubler is a software package that efficiently counts self-avoiding walks on lattices using length-doubling, symmetry exploitation, and parallel computation, enabling large-scale calculations within practical time and memory limits.

Contribution

The paper introduces SAWdoubler, a novel software tool that improves counting of self-avoiding walks through efficient algorithms, symmetry use, and parallelization, extending capabilities to larger N.

Findings

Z(28) computed in 1 hour 40 minutes on dual-core PC

Speedup of 1.56 with multicore parallelization

Symmetry exploitation reduces computation by a factor of 26

Abstract

This article presents SAWdoubler, a package for counting the total number Z(N) of self-avoiding walks (SAWs) on a regular lattice by the length-doubling method, of which the basic concept has been published previously by us. We discuss an algorithm for the creation of all SAWs of length N, efficient storage of these SAWs in a tree data structure, and an algorithm for the computation of correction terms to the count Z(2N) for SAWs of double length, removing all combinations of two intersecting single-length SAWs. We present an efficient numbering of the lattice sites that enables exploitation of symmetry and leads to a smaller tree data structure; this numbering is by increasing Euclidean distance from the origin of the lattice. Furthermore, we show how the computation can be parallelised by distributing the iterations of the main loop of the algorithm over the cores of a multicore architecture. Experimental results on the 3D cubic lattice demonstrate that Z(28) can be computed on a dual-core PC in only 1 hour and 40 minutes, with a speedup of 1.56 compared to the single-core computation and with a gain by using symmetry of a factor of 26. We present results for memory use and show how the computation is made to fit in 4 Gbyte RAM. It is easy to extend the SAWdoubler software to other lattices; it is publicly available under the GNU LGPL license.