Minimum Vertex-type Sequence Indexingfor Clusters on Square Lattice

TL;DR

This paper introduces a novel, orientation-independent indexing scheme called minimum vertex-type sequence for clusters on square lattices, enabling efficient structure comparison and congruence checks, with potential applications across various scientific fields.

Contribution

The paper proposes the minimum vertex-type sequence as a new indexing method that simplifies and improves cluster comparison on square lattices, generalizable to other high-symmetry lattices.

Findings

Orientation independence of the sequence

Efficient comparison involving only n pairs

Applicable to various high-symmetry lattices

Abstract

An effective indexing scheme for clusters that enables fast structure comparison and congruence check is desperately desirable in the field of mathematics, artificial intelligence, materials science, etc. Here we introduce the concept of minimum vertex-type sequence for the indexing of clusters on square lattice, which contains a series of integers each labeling the vertex type of an atom. The minimum vertex-type sequence is orientation independent, and it builds a one-to-one correspondence with the cluster. By using minimum vertex-type sequence for structural comparison and congruence check, only one type of data is involved, and the largest amount of data to be compared is n pairs, n is the cluster size. In comparison with traditional coordinate-based methods and distance-matrix methods, the minimum vertex-type sequence indexing scheme has many other remarkable advantages. Furthermore, this indexing scheme can be easily generalized to clusters on other high-symmetry lattices. Our work can facilitate cluster indexing and searching in various situations, it may inspire the search of other practical indexing schemes for handling clusters of large sizes.