A Simple, Compact and Dynamic Partition Scheme Based on Co-centric Spheres

Abstract

This paper describes the MB-tree, a symmetric data structure for the organization of multidimensional points. The proposed structure is based on a new partition scheme that divides the data space into cocentric partitions in an ‘onion’-like manner and ensures that partitions that are spatially successive in a multidimensional space are also successive in terms of their storage. Each partition is characterized from a distance from a fixed point and the resultant structure is k-d-cut, adaptable and brickwall. It has very efficient point search and adapts nicely to dynamic data spaces with high frequency of insertions and deletions and to non-uniformly distributed data. The organization is an extension of B-trees in order to index multidimensional data when the data space is metric. The indexing mechanism is organized as a B⁺-tree and compared to similar approaches the size of the index is minimum. Although the MB-tree has a simple structure, its performance compares to the one of other more complex indexes. We present the partition scheme and the index, describe its dynamic behavior, examine algorithms for several types of queries and provide experimental results.