Algorithms on Strings

Crochemore, Maxime; Hancart, Christophe; Lecroq, Thierry

doi:10.1017/cbo9780511546853

Cited by 326 publications

(318 citation statements)

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“…We introduce some standard notation; for further automata and stringology terminology, theory, algorithms and data structures see [CHL07,Smy03].…”

Section: Notationmentioning

confidence: 99%

Binary block order Rouen Transform

Daykin¹,

Groult²,

Guesnet³

et al. 2016

Theoretical Computer Science

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Please cite this article in press as: J.W. Daykin et al., Binary block order Rouen transform, Theoret. Comput. Sci. (2016), http://dx.doi.org/10.1016/j.tcs. 2016.05.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights• Novel twin binary Burrows-Wheeler type transforms are introduced.• The transforms are defined for Lyndon-like B-words which apply binary block order.• We call this approach the B-BWT Rouen Transform.• These bijective Rouen transforms and inverses are computed in linear time.• Preliminary experimental results indicate potential value of binary transforms. Binary Block Order Rouen Transform

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“…We introduce some standard notation; for further automata and stringology terminology, theory, algorithms and data structures see [CHL07,Smy03].…”

Section: Notationmentioning

confidence: 99%

Binary block order Rouen Transform

Daykin¹,

Groult²,

Guesnet³

et al. 2016

Theoretical Computer Science

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“…We use this algorithm later and it is explained in full detail in Section 5. This algorithm is linear : indeed, suffix standard permutation is equivalent to the suffix array of w, which may be computed in linear time [27]. Moreover, the sequence of left-to-right minima of a permutation is clearly computable in linear time.…”

Section: Lyndon Wordsmentioning

confidence: 99%

“…Moreover, the sequence of left-to-right minima of a permutation is clearly computable in linear time. This algorithm was known to Duval and Lefebvre ( [28], p. 250), who attribute it to Crochemore [27]. Note that suffix standardization may be used also to build the tree (or nonassociative word) associated to a Lyndon word, hence the associated Lie polynomial, which gives the Lyndon basis of the free Lie algebra (see [29]).…”

Section: Lyndon Wordsmentioning

confidence: 99%

Lyndon Christoffel digitally convex

Brlek

Lachaud

Provençal

et al. 2009

Pattern Recognition

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Discrete geometry redefines notions borrowed from Euclidean geometry creating a need for new algorithmical tools. The notion of convexity does not translate trivially, and detecting if a discrete region of the plane is convex requires a deeper analysis. To the many different approaches of digital convexity, we propose the combinatorics on words point of view, unnoticed until recently in the pattern recognition community. In this paper we provide first a fast optimal algorithm checking digital convexity of polyominoes coded by their contour word. The result is based on linear time algorithms for both computing the Lyndon factorization of the contour word, and the recognition of Christoffel factors that are approximations of digital lines. By avoiding arithmetical computations the algorithm is much simpler to implement and much faster in practice. We also consider the convex hull computation and relate previous work in combinatorics on words with the classical Melkman algorithm.

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“…The computation of the Suffix Array of y can be done in time O(n log n) in the comparison model [16] (see [3,6,9]). If the text is on an alphabet of integers in the range [0, n c ] for some constant c, the Suffix Array can be built in time O(n) [10,12,13,8] (see also [3]). …”

Section: Using a Suffix Arraymentioning

confidence: 99%

LPF Computation Revisited

Crochemore

Ilie

Iliopoulos

et al. 2009

Lecture Notes in Computer Science

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Abstract. We present efficient algorithms for storing past segments of a text. They are computed using two previously computed read-only arrays (SUF and LCP) composing the Suffix Array of the text. They compute the maximal length of the previous factor (subword) occurring at each position of the text in a table called LPF. This notion is central both in many conservative text compression techniques and in the most efficient algorithms for detecting motifs and repetitions occurring in a text. The main results are: a linear-time algorithm that computes explicitly the permutation that transforms the LCP table into the LPF table; a time-space optimal computation of the LPF table; and an O(n log n) strong in-place computation of the LPF table.

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Algorithms on Strings

Cited by 326 publications

References 0 publications

Binary block order Rouen Transform

Binary block order Rouen Transform

Lyndon Christoffel digitally convex

LPF Computation Revisited

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