O-trees: a constraint-based index structure

Constraint search trees are a generic approach to search trees where all operations are defined in terms of constraints. This abstract viewpoint makes clear the fundamental operations of search trees and immediately points to new possibilities for search trees. In this paper we present height-balanced constraint search trees (HCSTs), a general approach to building height-balanced index structures, and exemplify the approach with a new spatial index structure, the O-tree. An object in an O-tree is represented by constraints of the form ax_i+bx_j ⩽d where {a,b}⊆{-1,0,1} and x₁,...,x_n are the dimensions of the spatial data. We define the basic operations to build and search HCSTs, as well as constraint joins. We illustrate these algorithms using O-trees showing how the algorithms can make use of the more accurate information in the O-tree nodes. Experiments compare the IO-performance of the 2-dimensional O-tree with the R-tree