Department of Physics, South China University of Technology, Guangzhou, 510640, China.
Key Laboratory of Advanced Energy Storage Materials of Guangdong Province, South China University of Technology, Guangzhou, 510640, China.
Sci Rep. 2017 Mar 24;7(1):392. doi: 10.1038/s41598-017-00398-z.
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.
在数学、人工智能、材料科学等领域，人们迫切需要一种有效的聚类索引方案，以实现快速的结构比较和一致性检查。在这里，我们提出了一种基于正方形晶格上的聚类索引的最小顶点类型序列的概念，它包含一系列整数，每个整数标记一个原子的顶点类型。最小顶点类型序列是与方向无关的，它与聚类建立了一一对应的关系。通过使用最小顶点类型序列进行结构比较和一致性检查，只涉及一种类型的数据，并且要比较的最大数据量为 n 对，n 是聚类的大小。与传统的基于坐标的方法和距离矩阵方法相比，最小顶点类型序列索引方案具有许多其他显著的优点。此外，这种索引方案可以很容易地推广到其他高对称晶格上的聚类。我们的工作可以促进各种情况下的聚类索引和搜索，它可能会启发人们寻找其他处理大规模聚类的实用索引方案。
