On Data Partitioning in Tree Structure Metric-Space Indexes

Tree structure metric-space indexing methods recursively partition data according to their distances to a set of selected reference points (also called pivots). There are two basic forms of data partitioning: ball partition and General Hyper-plane (GH) partition. Most existing work only shows their superiority experimentally, and little theoretical proof is found. We propose an approach to unify existing data partitioning methods and analyze their performance theoretically. First, in theory, we unify the two basic forms of partitioning by proving that there are rotations of each other. Second, we show several theoretical or experimental results, which are able to indicate that ball partition outperforms GH partition. Our work takes a step forward in the theoretical study of metric-space indexing and is able to give a guideline of future index design.