Grammatical tree matching

Abstract

In structured text databases documents are represented as parse trees, and different tree matching notions can be used as primitives for query languages. Two useful notions of tree matching, tree inclusion and tree pattern matching both seem to require superlinear time. In this paper we give a general sufficient condition for a tree matching problem to be solvable in linear time, and apply it to tree pattern matching and tree inclusion. The application is based on the notion of a nonperiodic parse tree. We argue that most text documents can be modeled in a natural way using grammars yielding nonperiodic parse trees. We show how the knowledge that the target tree is nonperiodic can be used to obtain linear time algorithms for the tree matching problems. We also discuss the preprocessing of patterns for grammatical tree matching.