# Generalization of a suffix tree for RNA structural pattern matching

## Abstract

In molecular biology, it is said that two biological sequences tend to have similar properties if they have similar three-dimensional structures. Hence, it is very important to find not only similar sequences in the string sense, but also structurally similar sequences from databases. In this paper we propose a new data structure that is a generalization of a parameterized suffix tree (p-suffix tree for short) introduced by Baker. We call it the structural suffix tree or s-suffix tree for short. The s-suffix tree can be used for finding structurally related patterns of RNA or single-stranded DNA. Furthermore, we propose an O(n(log|∑| + log|Π|)) on-line algorithm for constructing it, where n is the sequence length, |∑| is the size of the normal alphabet, and |Π| is that of the alphabet called "parameter," which is related to the structure of the sequence. Our algorithm achieves linear time when it is used to analyze RNA and DNA sequences. Furthermore, as an algorithm for constructing the p-suffix tree, it is the first on-line algorithm, though the computing bound of our algorithm is the same as that of Kosaraju's best-known algorithm. The results of computational experiments using actual RNA and DNA sequences are also given to demonstrate our algorithm's practicality. © 2003 Springer-Verlag New York Inc.