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overlap-free split dimension

An overlap-free split dimension is a coordinate axis in a multidimensional spatial index structure along which an overflowing node can be partitioned into subsets whose resulting minimum bounding boxes share no volume. In high-dimensional data indexing, partitioning nodes along arbitrary axes often produces heavily overlapping bounding regions, forcing query algorithms to traverse multiple tree branches and substantially degrading search performance. An overlap-free split dimension is typically identified using the historical partitioning record of child nodes, ensuring that a dividing boundary placed perpendicular to that axis creates completely disjoint bounding boxes. If an index structure cannot find an overlap-free split dimension that satisfies node balance constraints, it may avoid the split entirely by enlarging the node into a supernode to prevent high directory overlap.

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The X-tree : An Index Structure for High-Dimensional Data

The X-tree : An Index Structure for High-Dimensional Data

S. Berchtold, D. Keim, H. Kriegel

OrganizationsLudwig Maximilian University of Munich

Why you should read this

Introduces the X-tree, an efficient high-dimensional indexing structure that avoids bounding-box overlap by combining an overlap-minimizing split algorithm with variable-sized supernodes to outperform standard R*-trees and TV-trees by orders of magnitude.

In this paper, we propose a new method for indexing large amounts of point and spatial data in high-dimensional space. An analysis shows that index structures such as the R*-tree are not adequate for indexing high-dimensional data sets. The major problem of R-tree-based index structures is the overlap of the bounding boxes in the directory, which increases with growing dimension. To avoid this problem, we introduce a new organization of the directory which uses a split algorithm minimizing overlap and additionally utilizes the concept of supernodes. The basic idea of overlap-minimizing split and supernodes is to keep the directory as hierarchical as possible, and at the same time to avoid splits in the directory that would result in high overlap. Our experiments show that for high-dimensional data, the X-tree outperforms the well-known R*-tree and the TV-tree by up to two orders of magnitude.

Added

2026-09-24