Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points

Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 (2024) Polynomial-Time Algorithms for Continuous Metrics on Atomic Clouds of Unordered Points. Match - Communications in Mathematical and in Computer Chemistry, 91 (1). pp. 79-108.

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Official URL: http://dx.doi.org/10.46793/match.91-1.079k

Abstract

<jats:p>The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a composition of translations and rotations. The existing datasets of experimental and simulated molecules require a continuous quantification of similarity in terms of a distance metric. While clouds of m ordered points were continuously classified by Lagrange’s quadratic forms (distance matrices or Gram matrices), their extensions to m unordered points are impractical due to the exponential number of m! permutations. We propose new metrics that are continuous in general position and are computable in a polynomial time in the number m of unordered points in any Euclidean space of a fixed dimension n.</jats:p>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	04 Oct 2023 08:09
Last Modified:	08 Jan 2024 12:34
DOI:	10.46793/match.91-1.079k
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3173401