K-means Split Revisited: Well-grounded Approach and Experimental Evaluation

Abstract

R-tree is a data structure used for multidimensional indexing. Essentially, it is a balanced tree consisting of nested hyper-rectangles which are used to locate the data. One of the most performance sensitive parts of this data structure is its split algorithm, which runs during node overflows. The split can be performed in multiple ways, according to many different criteria and in general the problem of finding an optimal solution is NP-hard. There are many heuristic split algorithms. In this paper we study an existing k-means node split algorithm. We describe a number of serious issues in its theoretical foundation, which made us to re-design k-means split. We propose several well-grounded solutions to the re-emerged problem of k-means split. Finally, we report the comparison results using PostgreSQL and contemporary benchmark for multidimensional structures.