Tree String Path Subsequences Automaton and Its Use for Indexing XML Documents

Abstract

The theory of indexing texts is well-researched, which does not hold for indexing other data structures, such as trees for example. In this paper a simple method of indexing a tree for subsequences of string paths in the tree by finite automaton is presented. The use of the index is shown on indexing XML documents for XPath descendant-or-self axis inspired queries. Given a subject tree $\mathcal{T}$ with n nodes, the tree is preprocessed and an index, which is a directed acyclic subsequence graph for a set of strings, is constructed. The searching phase uses the index, reads an input string path subsequence $\mathcal{Q}$ inspired by the specific XPath query of size m and computes the list of positions of all occurrences of $\mathcal{Q}$ in the tree $\mathcal{T}$. The searching is performed in time $\mathcal {O}(m)$ and does not depend on n. Although the number of distinct valid queries is $\mathcal {O}(2^n)$, the size of the index is $\mathcal {O}(h^k)$, where h is the height of the tree $\mathcal{T}$ and k is the number of its leaves. Moreover, we discuss that in the case of indexing a common XML document the size of the index is even smaller $\mathcal {O}(h \cdot 2^k)$.

J. Janoušek—This research has been partially supported by the Czech Science Foundation (GAČR) as project No. GA-13-03253S and by Technology Agency of the Czech Republic (TAČR) as project No. TA03010964 in $\alpha$ programme.