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

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

doi:10.1016/j.ipl.2019.03.003

Cited by 7 publications

(3 citation statements)

References 6 publications

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“…Remark 16. Indeed, given a regular pattern and a string x containing Q indeterminate letters (a case considered in both [4] and [5]), KMP Indet may make as many as mQ shifts, each requiring O(m 2 ) processing, thus O(m 3 Q)…”

Section: Lemma 12 ([12]mentioning

confidence: 99%

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Practical KMP/BM Style Pattern-Matching on Indeterminate Strings

Dehghani¹,

Mhaskar²,

Smyth³

2022

Preprint

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In this paper we describe two simple, fast, space-efficient algorithms for finding all matches of an indeterminate pattern p = p[1..m] in an indeterminate stringwhere both p and x are defined on a "small" ordered alphabet Σ -say, σ = |Σ| ≤ 9. Both algorithms depend on a preprocessing phase that replaces Σ by an integer alphabet Σ I of size σ I = σ which (reversibly, in time linear in string length) maps both x and p into equivalent regular strings y and q, respectively, on Σ I , whose maximum (indeterminate) letter can be expressed in a 32-bit word (for σ ≤ 4, thus for DNA sequences, an 8-bit representation suffices). We first describe an efficient version KMP Indet of the venerable Knuth-Morris-Pratt algorithm to find all occurrences of q in y (that is, of p in x), but, whenever necessary, using the prefix array, rather than the border array, to control shifts of the transformed pattern q along the transformed string y.We go on to describe a similar efficient version BM Indet of the Boyer-Moore algorithm that turns out to execute significantly faster than KMP Indet over a wide range of test cases. We conjecture that a similar approach may yield practical and efficient indeterminate equivalents to other well-known patternmatching algorithms, in particular the several variants of Boyer-Moore.

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Section: Lemma 12 ([12]mentioning

confidence: 99%

“…Thus, in many cases, cumbersome and time-consuming matches of indeterminate letters can be efficiently handled. For background on pattern-matching in indeterminate strings, see [6,1,8,11,9,2,16,17,4,5].…”

Section: Introductionmentioning

confidence: 99%

Practical KMP/BM Style Pattern-Matching on Indeterminate Strings

Dehghani¹,

Mhaskar²,

Smyth³

2022

Preprint

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“…Example 6.1) to relabel the sets and order the degenerate strings in the D-BWT matrix. Subsequently in [18], the D-BWT was applied to pattern matching using the backward search technique. This formalized and extended work implemented in [32] presenting a bioinformatics software tool, BWBBLE, for pattern matching on a pan-genome that they called a reference multi-genome.…”

Section: Applications On Meta Stringsmentioning

confidence: 99%

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Daykin,

Köppl,

Kübel

et al. 2021

Preprint

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We characterize those strings whose suffix arrays are based on arithmetic progressions, in particular, arithmetically progressed permutations where all pairs of successive entries of the permutation have the same difference modulo the respective string length. We show that an arithmetically progressed permutation P coincides with the suffix array of a unary, binary, or ternary string. We further analyze the conditions of a given P under which we can find a uniquely defined string over either a binary or ternary alphabet having P as its suffix array. For the binary case, we show its connection to lower Christoffel words, balanced words, and Fibonacci words. In addition to solving the arithmetically progressed suffix array problem, we give the shape of the Burrows-Wheeler transform of those strings solving this problem. These results give rise to numerous future research directions.

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