Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice

Longguang Liao,Yu-Jun Zhao,Zexian Cao,Xiao-Bao Yang

doi:10.1038/s41598-017-00398-z

Longguang Liao, Yu-Jun Zhao + Show 2 more

Open Access

https://doi.org/10.1038/s41598-017-00398-z

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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.

Highlights

The size and structure are the fundamental factors in determining the properties of a cluster, they are of great concern in the study and application of clusters
For 2D and 3D high-symmetry crystal-fragment clusters, where the interatomic distances among the nearest neighboring atoms are fixed, there is another recognition technique based on the relative orientations of the bonds, which employs codes obtained by using the Balaban and von Schleyer’s technique[40, 41]
In the current work we introduce a new indexing scheme, the minimum vertex-type sequence, to label and characterize the clusters on square lattice, which might meet some requirements for fast and effective decision making of artificial intelligence as in the game of Go42

Summary

Indexing for Clusters on Square

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. For 2D and 3D high-symmetry crystal-fragment clusters, where the interatomic distances among the nearest neighboring atoms are fixed, there is another recognition technique based on the relative orientations of the bonds, which employs codes obtained by using the Balaban and von Schleyer’s technique[40, 41] In this approach the largest amount of comparing data is reduced to (n − 1) pairs, it is, not a fast structure retrieval method since finding the main and side chains of a given structure is very time-consuming. In the current work we introduce a new indexing scheme, the minimum vertex-type sequence, to label and characterize the clusters on square lattice (below often referred to as cluster when no ambiguity may arise), which might meet some requirements for fast and effective decision making of artificial intelligence as in the game of Go42 This indexing scheme employs only the vertex type, or precisely the nearest-neighbor configuration, for each atom in a cluster. For clusters of size n, the largest amount of comparing data for congruency check is only n pairs

Results

Complexity of data sampling easy easy hard easy

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