A Note on Easy and Efficient Computation of Full Abelian Periods of a Word

Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.Comment: Accepted for publication in Discrete Applied Mathematic

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

International audienceA 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, 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 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 complexity time is O(qm2). Experimental results show that our method performs well in practice

Practical fast on-line exact pattern matching algorithms for highly similar sequences

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Fast practical online exact single and multiple pattern matching algorithms in highly similar sequences

International audienceWith the advent of high-throughput sequencing technologies there are more and more genomic sequences of individuals of the same species available. These sequences only differ by a very small amount of variations. There is thus a strong need for efficient algorithms for performing fast pattern matching in such specific sets of sequences. In this paper, we propose efficient practical algorithms that solve on-line exact pattern matching problem in a set of highly similar DNA sequences. We first present a method for exact single pattern matching when k variations are allowed in a window which size is equal to the pattern length. We then propose an algorithm for exact multiple pattern matching when only one variation is allowed in a window which size is equal to the length of the longest pattern. Experimental results show that our algorithms, though not optimal in the worst case, have good performances in practice