Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice

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 clus...

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Autores principales:	Longguang Liao, Yu-Jun Zhao, Zexian Cao, Xiao-Bao Yang
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/552d477d692b4d079a48263d43a0fab2
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spelling	oai:doaj.org-article:552d477d692b4d079a48263d43a0fab22021-12-02T16:07:06ZMinimum Vertex-type Sequence Indexing for Clusters on Square Lattice10.1038/s41598-017-00398-z2045-2322https://doaj.org/article/552d477d692b4d079a48263d43a0fab22017-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-00398-zhttps://doaj.org/toc/2045-2322Abstract 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.Longguang LiaoYu-Jun ZhaoZexian CaoXiao-Bao YangNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-6 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Longguang Liao Yu-Jun Zhao Zexian Cao Xiao-Bao Yang Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice
description	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.
format	article
author	Longguang Liao Yu-Jun Zhao Zexian Cao Xiao-Bao Yang
author_facet	Longguang Liao Yu-Jun Zhao Zexian Cao Xiao-Bao Yang
author_sort	Longguang Liao
title	Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice
title_short	Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice
title_full	Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice
title_fullStr	Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice
title_full_unstemmed	Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice
title_sort	minimum vertex-type sequence indexing for clusters on square lattice
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/552d477d692b4d079a48263d43a0fab2
work_keys_str_mv	AT longguangliao minimumvertextypesequenceindexingforclustersonsquarelattice AT yujunzhao minimumvertextypesequenceindexingforclustersonsquarelattice AT zexiancao minimumvertextypesequenceindexingforclustersonsquarelattice AT xiaobaoyang minimumvertextypesequenceindexingforclustersonsquarelattice
_version_	1718384717099696128

Minimum Vertex-type Sequence Indexing for Clusters on Square Lattice

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