On Optimal Multiversion Access Structures

We propose an asymptotically optimal multiversion B-tree. In our setting, insertions and deletions of data items are allowed only for the present version, whereas range queries and exact match queries are allowed for any version, present or past. The technique we present for transforming a (usual single version) B-tree into a multiversion B-tree is more general: it applies to a number of spatial and non-spatial hierarchical external access structures with certain properties directly, and it can be modiied for others. For the B-tree and several other hierarchical external access structures, multiversion capabilities come at no extra cost, neither for storage space nor for runtime, asymptotically in the worst case. The analysis of the behavior of the multiversion B-tree shows that the constant loss of eeciency is low enough to make our suggestion not only a theoretical, but also a practical one.