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

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