Tree template matching in ranked ordered trees by pushdown automata

• Published in: Journal of discrete algorithms (Amsterdam, Netherlands) Vol. 17; pp. 15 - 23
• Main Authors: Flouri, Tomáš, Iliopoulos, Costas S., Janoušek, Jan, Melichar, Bořivoj, Pissis, Solon P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2012
• Subjects: Algorithms on strings; Automata theory; Tree pattern matching; Automata theory; Algorithms on strings; Tree pattern matching
• ISSN: 1570-8667; 1570-8675
• DOI: 10.1016/j.jda.2012.10.003

We consider the problem of tree template matching in ranked ordered trees, and propose a solution based on the bottom-up technique. Specifically, we transform the tree pattern matching problem to a string matching problem, by transforming the tree template and the subject tree to strings representing their postfix notation, and then use pushdown automata as the computational model. The method is analogous to the construction of string pattern matchers. The given tree template is preprocessed once, by constructing a nondeterministic pushdown automaton, which is then transformed to the equivalent deterministic one. Although we prove that the space required for preprocessing is exponential to the size of the tree template in the worst case, the space required for a specific class of tree templates is linear. The time required for the searching phase is linear to the size of the subject tree in both cases.