Indeterminate String Factorizations and Degenerate Text Transformations

Daykin, Jacqueline W.; Watson, Bruce W.

doi:10.1007/s11786-016-0285-x

Cited by 5 publications

(3 citation statements)

References 37 publications

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“…Daykin and Watson proposed a simple degenerate BWT, the D-BWT [21], constructed by applying lex-extension order (cf. Example 6.1) to relabel the sets and order the degenerate strings in the D-BWT matrix.…”

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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Section: Applications On Meta Stringsmentioning

confidence: 99%

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

Daykin,

Köppl,

Kübel

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In [4], Daykin and Watson present a simple modification of the classic BWT, the degenerate Burrows-Wheeler transform, which is suitable for clustering degenerate strings.…”

Section: Notation and Definitionsmentioning

confidence: 99%

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

Daykin

Groult

Guesnet

et al. 2019

Information Processing Letters

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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, 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 patternmatching 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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“…Do not confuse bucket orders with indeterminate strings (also known as degenerate string) which are strings involving uncertainty and consist of nonempty subsets of letters over an alphabet Σ [25, 26]. In such strings the same character may appear in several subsets while it is not the case in bucket orders.…”

Section: Definitions and Notationsmentioning

confidence: 99%

Efficient algorithms for Longest Common Subsequence of two bucket orders to speed up pairwise genetic map comparison

2018

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Genetic maps order genetic markers along chromosomes. They are, for instance, extensively used in marker-assisted selection to accelerate breeding programs. Even for the same species, people often have to deal with several alternative maps obtained using different ordering methods or different datasets, e.g. resulting from different segregating populations. Having efficient tools to identify the consistency and discrepancy of alternative maps is thus essential to facilitate genetic map comparisons. We propose to encode genetic maps by bucket order, a kind of order, which takes into account the blurred parts of the marker order while being an efficient data structure to achieve low complexity algorithms. The main result of this paper is an O(n log(n)) procedure to identify the largest agreements between two bucket orders of n elements, their Longest Common Subsequence (LCS), providing an efficient solution to highlight discrepancies between two genetic maps. The LCS of two maps, being the largest set of their collinear markers, is used as a building block to compute pairwise map congruence, to visually emphasize maker collinearity and in some scaffolding methods relying on genetic maps to improve genome assembly. As the LCS computation is a key subroutine of all these genetic map related tools, replacing the current LCS subroutine of those methods by ours –to do the exact same work but faster– could significantly speed up those methods without changing their accuracy. To ease such transition we provide all required algorithmic details in this self contained paper as well as an R package implementing them, named LCSLCIS, which is freely available at: https://github.com/holtzy/LCSLCIS.

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Indeterminate String Factorizations and Degenerate Text Transformations

Cited by 5 publications

References 37 publications

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

On Arithmetically Progressed Suffix Arrays and related Burrows-Wheeler Transforms

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

Efficient algorithms for Longest Common Subsequence of two bucket orders to speed up pairwise genetic map comparison

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