On the Complexity of BV-tree Updates

In [Fre95b] we discussed the use of multi-dimensional index methods in constraint databases. In [Fre95a] we showed how to overcome a fundamental problem which has afflicted all multi-dimensional indexing techniques based on the recursive partitioning of a dataspace: how to build the partition hierarchy so that the location of each object in the hierarchy is specified unambiguously (i.e. each object can always be located in a shortest path search from root to leaf), while at the same time maintaining a guaranteed minimum occupancy and thus number of branches (fan-out ratio f ) of every node in the hierarchy.