Topology B-Trees and Their Applications

The well-known B-tree data structure provides a mechanism for dynamically maintaining balanced binary trees in external memory. We present an external-memory dynamic data structure for maintaining arbitrary binary trees. Our data structure, which we call the topology B-tree, is an external-memory analogue to the internal-memory topol-ogy tree data structure of Frederickson. It allows for dynamic expression evaluation and updates as well as various tree searching and evaluation queries. We show how to apply this data structure to a number of external-memory dynamic problems, including approximate nearest-neighbor searching and closest-pair maintenance.