A new characterization of maximal repetitions by Lyndon trees

Bannai, Hideo; Tomohiro, I; Inenaga, Shunsuke; Nakashima, Yuto; Takeda, Masayuki; Tsuruta, Kenji

doi:10.1137/1.9781611973730.38

Cited by 32 publications

(56 citation statements)

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“…The following is a part of Proposition In the next part of the paper we will implicitly refer to totally ordered alphabets. For two nonempty words x, y, we write x ≪ y if x ≺ y and x is not a proper prefix of y [2]. We also write y ≻ x if x ≺ y.…”

Section: Wordsmentioning

confidence: 99%

Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words

Bonizzoni

Felice

Zaccagnino

et al. 2020

Language and Automata Theory and Applications

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Lyndon words have been largely investigated and showned to be a useful tool to prove interesting combinatorial properties of words. In this paper we state new properties of both Lyndon and inverse Lyndon factorizations of a word w, with the aim of exploring their use in some classical queries on w.The main property we prove is related to a classical query on words. We prove that there are relations between the length of the longest common extension (or longest common prefix) lcp(x, y) of two different suffixes x, y of a word w and the maximum length M of two consecutive factors of the inverse Lyndon factorization of w. More precisely, M is an upper bound on the length of lcp(x, y). This result is in some sense stronger than the compatibility property, proved by Mantaci, Restivo, Rosone and Sciortino for the Lyndon factorization and here for the inverse Lyndon factorization. Roughly, the compatibility property allows us to extend the mutual order between local suffixes of (inverse) Lyndon factors to the suffixes of the whole word.A main tool used in the proof of the above results is a property that we state for factors m i with nonempty borders in an inverse Lyndon factorization: a nonempty border of m i cannot be a prefix of the next factor m i+1 . The last property we prove shows that if two words share a common overlap, then their Lyndon factorizations can be used to capture the common overlap of the two words.The above results open to the study of new applications of Lyndon words and inverse Lyndon words in the field of string comparison.

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Section: Wordsmentioning

confidence: 99%

Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words

Bonizzoni

Felice

Zaccagnino

et al. 2020

Language and Automata Theory and Applications

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“…Several improvements on the upper bound can be found in [16,4,14,5,8]. Kolpakov and Kucherov conjectured that this number is in fact smaller than n, which has been proved by Bannai et al [1,2]. Recently, Holub [10] and Fischer et al [9] gave a tighter upper bound reaching 22n/23.…”

Section: Introductionmentioning

confidence: 99%

On the density of Lyndon roots in factors

Crochemore¹,

Mercaş²

2016

Theoretical Computer Science

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“…The term "Lyndon array" was apparently introduced in [2], essentially equivalent to the "Lyndon tree" of Hohlweg & Reutenauer [3]. Interest in Lyndon arrays has been sparked by the surprising characterization of runs through Lyndon words by Bannai et al [4], who were thus able to resolve the long-standing conjecture that the number of runs (maximal periodicities) in any string of length n is less than n.…”

Section: Introductionmentioning

confidence: 99%

Lyndon array construction during Burrows–Wheeler inversion

Louza

Smyth

Manzini

et al. 2018

Journal of Discrete Algorithms

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In this paper we present an algorithm to compute the Lyndon array of a string T of length n as a byproduct of the inversion of the Burrows-Wheeler transform of T . Our algorithm runs in linear time using only a stack in addition to the data structures used for Burrows-Wheeler inversion. We compare our algorithm with two other linear-time algorithms for Lyndon array construction and show that computing the Burrows-Wheeler transform and then constructing the Lyndon array is competitive compared to the known approaches. We also propose a new balanced parenthesis representation for the Lyndon array that uses 2n + o(n) bits of space and supports constant time access. This representation can be built in linear time using O(n) words of space, or in O(n log n/ log log n) time using asymptotically the same space as T .

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A new characterization of maximal repetitions by Lyndon trees

Cited by 32 publications

References 0 publications

Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words

Lyndon Words versus Inverse Lyndon Words: Queries on Suffixes and Bordered Words

On the density of Lyndon roots in factors

Lyndon array construction during Burrows–Wheeler inversion

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