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 W. Watson · Information Processing Letters · 2019
A degenerate or indeterminate string on an alphabet Σ is a sequence of non-empty subsets of Σ. Given a degenerate string t of length n and its Burrows–Wheeler transform we present a new method for searching for a degenerate pattern of length m in t running in O ( m n ) time on a constant size alphabet Σ. 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 time complexity is O ( q m 2 ) for counting the number of occurrences and O ( q m 2 + occ ) for reporting the found occurrences where occ is the number of occurrences of the pattern in t . Experimental results show that our method performs well in practice.