A Full and Linear Index of a Tree for Tree Patterns

Abstract

A new and simple method of indexing a tree for tree patterns is presented. A tree pattern is a tree whose leaves can be labelled by a special symbol S, which serves as a placeholder for any subtree. Given a subject tree T with n nodes, the tree is preprocessed and an index, which consists of a standard string compact suffix automaton and a subtree jump table, is constructed. The number of distinct tree patterns which match the tree is $\mathcal{O}(2^n)$, and the size of the index is $\mathcal{O}(n)$. The searching phase uses the index, reads an input tree pattern P of size m and computes the list of positions of all occurrences of the pattern P in the tree T. For an input tree pattern P in linear prefix notation pref(P) = P ₁ S P ₂ S …S P _k , k ≥ 1, the searching is performed in time $\mathcal{O}(m + \sum\limits_{i=1}^k |occ(P_i)|))$, where occ(P _i ) is the set of all occurrences of P _i in pref(T).