Unordered tree matching and ordered tree matching: the evaluation of tree pattern queries

Abstract

In this paper, we study the twig pattern matching in XML document databases. Two algorithms A1 and A2 are discussed according to two different definitions of tree embedding. By the first definition, only the ancestor-descendant relationship is considered. By the second one, we take not only the ancestor-descendant relationship, but also the order of siblings into account. Both A1 and A2 are based on a subtree reconstruction technique, by which a tree structure is reconstructed according to a given set of data streams. More importantly, by revealing an interesting property of tree encoding, we show that the subtree reconstruction can be easily extended to a strategy (i.e., A1) for checking subtree matching according to the first definition with any kind of path join or join-like operations being completely avoided. A2 needs more time and space since it deals with a more difficult problem, but without join operations involved, either. The computational complexities of both algorithms are analysed, showing that they have a better performance than any existing strategy for this problem.

A Linear-Space Top-Down Algorithm for Tree Inclusion Problem

“…The ordered tree inclusion problem was initially introduced by Knuth [10], where only a sufficient condition for this problem is given. The tree inclusion has been suggested as an important primitive for expressing queries on structured document databases [4,5,6,12]. A structured document database is considered as a collection of parse trees that represent the structure of the stored texts and the tree inclusion is used as a means of retrieving information from them.…”