Similarity of particle systems using an invariant root mean square deviation measure

TL;DR

This paper introduces an algorithm for testing similarity between finite particle systems that is invariant under permutations, rotations, and translations, utilizing an invariant RMSD measure to find the optimal alignment efficiently.

Contribution

The paper presents a novel algorithm that computes an invariant RMSD for particle systems and finds the globally optimal alignment in cubic time.

Findings

Algorithm efficiently tests particle system similarity.

It finds the optimal alignment in O(n^3) operations.

The method is invariant under permutations, rotations, and translations.

Abstract

Determining whether two particle systems are similar is a common problem in particle simulations. When the comparison should be invariant under permutations, orthogonal transformations, and translations of the systems, special techniques are needed. We present an algorithm that can test particle systems of finite size for similarity and, if they are similar, can find the optimal alignment between them. Our approach is based on an invariant version of the root mean square deviation (RMSD) measure and is capable of finding the globally optimal solution in $O(n^3)$ operations where $n$ is the number of three-dimensional particles.