The BIRD Numbering Scheme for XML and Tree Databases - Deciding and Reconstructing Tree Relations Using Efficient Arithmetic Operations

We introduce a family of numbering schemes for the nodes of tree databases that are based on a structural summary for the database, such as the DataGuide. Using such a scheme, given the node IDs of two database nodes and the corresponding nodes in the structural summary we may decide the extended XPath relations Child, Child, Child∗, Following, NextSibling, NextSibling, NextSibling∗ for the nodes without access to the database. Similarly we can reconstruct the parent node and neighboured siblings of a given node. All decision and reconstruction steps are based on simple arithmetic operations. The BIRD scheme offers high expressivity and needs modest storage capacities. Compared to other identification schemes with similar expressivity, BIRD performs best in terms of both storage consumption and execution time for decision and reconstruction. A very attractive feature of the BIRD scheme is that all extended XPath relations can be decided and reconstructed in constant time, i.e. independent of tree position and distance of the nodes involved.