Partially Persistent Search Trees with Transcript Operations

When balanced binary search trees are made partially persistent using the node-copying method [5], the possibility of searching efficiently for information in the past is added to the system. The operations of updating the present version and searching in the present as well as in the past are asymptotically as efficient as in the corresponding normal (non-persistent) binary search tree. In database applications, it is sometimes desirable to produce transcripts of information change over time. If we wish to obtain a transcript of information related to some key k from version number v1 to v2, this can be obtained by independent search operations in all versions in that interval in time O ph , where h is the maximum height of the search tree in that interval, and p v2 v1 1 is the number of versions between v1 and v2. We discuss when and how this can be reduced to O h p by maintaining one extra pointer with a version number in each node, without changing the asymptotic complexity of any of the existing operations. In database applications, search trees are usually leaf-oriented, which means that all keys reside in the leaves, and internal nodes contain routers guiding the search to the correct leaf. Leaves are often of another type than the internal nodes, and contain extra pointers or space consuming values associated with