Efficient pattern matching in degenerate strings with the Burrows-Wheeler transform

Jacqueline W. Daykin, Richard Groult, Yannick Guesnet, Thierry Lecroq, Arnaud Lefebvre, Martine Léonard, Laurent Mouchard, Élise Prieur-Gaston, Bruce Watson

A degenerate or indeterminate string on an alphabet $\Sigma$ is a sequence of non-empty subsets of $\Sigma$. Given a degenerate string $t$ of length $n$, we present a new method based on the Burrows--Wheeler transform for searching for a degenerate pattern of length $m$ in $t$ running in $O(mn)$ time on a constant size alphabet $\Sigma$. Furthermore, it is a hybrid pattern-matching technique that works on both regular and degenerate strings. A degenerate string is said to be conservative if its number of non-solid letters is upper-bounded by a fixed positive constant $q$; in this case we show that the search complexity time is $O(qm^2)$. Experimental results show that our method performs well in practice.

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