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

This paper introduces the BIRD family of numbering schemes for tree databases, which is based on a structural summary such as the DataGuide. Given the BIRD IDs of two database nodes and the corresponding nodes in the structural summary we 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 neighbouring siblings of a given node. All decision and reconstruction steps are based on simple arithmetic operations. The BIRD scheme offers high expressivity and efficiency paired with modest storage demands. Compared to other identification schemes with similar expressivity, BIRD performs best in terms of both storage consumption and execution time, with experiments underlining the crucial role of ID reconstruction in query evaluation. 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. All results are shown to scale up to the multi-Gigabyte level.