The universal B-tree for multidimensional indexing: General concepts

Abstract

Today almost all database systems use B-trees as their main access method. One of the main drawbacks of the classical B-tree is, however, that it works well only for one-dimensional data. In this paper we present a new access structure, called UB-tree (for universal B-tree) for multidimensional data. The UB-tree is balanced and has all the guaranteed performance characteristics of B-trees, i.e. it requires linear space for storage and logarithmic time for the basic operations of INSERT FIND DELETE. In addition the UB-tree has the fundamental property, that it preserves clustering of objects w.r. to Cartesian distance. Therefore, the UB-tree shows its main strengths for multidimensional data. It has very high potential for parallel processing. With the new method, a single UB-tree can replace an arbitrary number of secondary indexes. For updates this means that only one UB-tree must be managed instead of several secondary indexes. This reduces runtime and storage requirements substantially. For queries and in particular range queries the UB-tree has multiplicative complexity instead of the additive complexity of multiple secondary indexes. This results in dramatic performance improvements over secondary indexes. The UB-tree is obviously useful for geometric databases, datawarehousing and datamining applications, but even more for databases in general, where multiple secondary indexes are widespread~ which can all be replaced by a single UB-tree index.