Tree patterns form a natural basis to query tree-structured data such as XML and LDAP. To improve the efficiency of tree pattern matching, it is essential to quickly identify and eliminate redundant nodes in the pattern. In this paper, we study tree pattern minimization both in the absence and in the presence of integrity constraints (ICs) on the underlying tree-structured database. In the absence of ICs, we develop a polynomial-time query minimization algorithm called CIM, whose efficiency stems from two key properties: (i) a node cannot be redundant unless its children are; and (ii) the order of elimination of redundant nodes is immaterial. When ICs are considered for minimization, we develop a technique for query minimization based on three fundamental operations: augmentation (an adaptation of the well-known chase procedure), minimization (based on homomorphism techniques), and reduction. We show the surprising result that the algorithm, referred to as ACIM, obtained by first augmenting the tree pattern using ICs, and then applying CIM, always finds the unique minimal equivalent query. While ACIM is polynomial time, it can be expensive in practice because of its inherent non-locality. We then present a fast algorithm, CDM, that identifies and eliminates local redundancies due to ICs, based on propagating ”information labels” up the tree pattern. CDM can be applied prior to ACIM for improving the minimization efficiency. We complement our analytical results with an experimental study that shows the effectiveness of our tree pattern minimization techniques.
