We propose a data structure in d-dimensional hyperbolic space that can be
considered a natural counterpart to quadtrees in Euclidean spaces. Based on
this data structure we propose a so-called L-order for hyperbolic point sets,
which is an extension of the Z-order defined in Euclidean spaces. We
demonstrate the usefulness of our hyperbolic quadtree data structure by giving
an algorithm for constant-approximate closest pair and dynamic
constant-approximate nearest neighbours in hyperbolic space of constant
dimension d