Dotted Suffix Trees A Structure for Approximate Text Indexing

Abstract

In this work, the problem we address is text indexing for approximate matching. Given a text $\mathcal{T}$ which undergoes some preprocessing to generate an index, we can later query this index to identify the places where a string occurs up to a certain number of errors k (edition distance). The indexing structure occupies space $\mathcal{O}(n\log^kn)$ in the average case, independent of alphabet size. This structure can be used to report the existence of a match with k errors in $\mathcal{O}(3^k m^{k+1})$ and to report the occurrences in $\mathcal{O}(3^k m^{k+1} + \mbox{\it ed})$ time, where m is the length of the pattern and ed and the number of matching edit scripts. The construction of the structure has time bound by $\mathcal{O}(kN|\Sigma|)$, where N is the number of nodes in the index and |Σ| the alphabet size.