Tighter Bounds and Optimal Algorithms for All Maximal α-gapped Repeats and Palindromes

Gawrychowski, Paweł; Tomohiro, I; Inenaga, Shunsuke; Köppl, Dominik; Manea, Florín

doi:10.1007/s00224-017-9794-5

Cited by 20 publications

(5 citation statements)

References 20 publications

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“…In particular, any α-gapped repeat can be extended to a uniquely defined maximal α-gapped or overlapped repeat. In [21,22], the following fact on maximal α-gapped repeats was obtained. Theorem 3.…”

Section: Repeatsmentioning

confidence: 91%

“…In [22], the more precise upper bound 18αn on the number of maximal α-gapped repeats in w was actually obtained. A tighter bound on this number was obtained later in [24].…”

Section: Repeatsmentioning

confidence: 99%

“…In [20], the expected time of the second algorithm was improved to the linear bound O( n δ 2 log 1 δ ). Using the results of [21,22], this time can be further improved to O( n δ log 1 δ ). In [23], it is shown that all subrepetitions with the largest exponent (over all subrepetitions) in an overlap-free string can be found in O(n) time for a constant-size alphabet.…”

Section: Introductionmentioning

confidence: 99%

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Almost Optimal Searching of Maximal Subrepetitions in a Word

Kolpakov

2022

Mathematics

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For some fixed δ such that 0<δ<1, a δ-subrepetition in a word is a factor whose exponent is less than 2 but is not less than 1+δ (the exponent of the factor is the ratio of the factor length to its minimal period). The δ-subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter while preserving its minimal period. In the paper, we propose an algorithm for searching all maximal δ-subrepetitions in a word of length n in O(nδlog1δ) time (the lower bound for this time is Ω(nδ)). It improves the previous known time complexity bounds for solving this problem.

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Section: Repeatsmentioning

confidence: 91%

“…In [22], the more precise upper bound 18αn on the number of maximal α-gapped repeats in w was actually obtained. A tighter bound on this number was obtained later in [24].…”

Section: Repeatsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Almost Optimal Searching of Maximal Subrepetitions in a Word

Kolpakov

2022

Mathematics

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“…Palindromes are strings that read the same forward and backward. Finding palindromic structures in a given string is a fundamental task in string processing, and thus it has extensively been studied (e.g., see [1][2][3][4][5][6][7][8][9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Computing palindromes and suffix trees of dynamic trees

Funakoshi,

Mieno,

Nakashima

et al. 2024

Preprint

Self Cite

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We consider the problems of computing maximal palindromes and distinct palindromes in an edge-labeled rooted tree where each edge is labeled by a single character. Such a tree is a natural generalization of a string, which can be seen as a single-path tree. There is a linear time offline algorithm to compute maximal palindromes and distinct palindromes in a given (static) tree whose edge-labels are drawn from a linearly-sortable alphabet [Mieno et al., ISAAC 2022]. In this paper, we tackle problems of palindrome enumeration on dynamic trees which support leaf additions and leaf deletions. We propose the first sub-quadratic algorithms to enumerate palindromes in a dynamic tree whose edge-labels are drawn from a general ordered alphabet. Our algorithm computes all maximal palindromes in O(N log h) time and all distinct palindromes in O(N log h + N log s) time with O(N) working space, where N is the number of edges in the tree, h is the height of the tree, and s is the number of distinct characters appearing in the tree. Furthermore, as a by-product, we present an O(N log N)-time online algorithm to construct the suffix tree of the input tree, which is of independent interest.

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“…It is maximal if the two occurrences of u in it cannot be extended simultaneously with the same letter to the right nor to the left. Gawrychowski et al [10] proved that there are words that have Θ(αn) maximal α-gapped repeats.…”

Section: Introductionmentioning

confidence: 99%

Maximal Closed Substrings

Badkobeh

Luca²,

Fici³

et al. 2022

Lecture Notes in Computer Science

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A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a maximal closed substring (MCS), which is an occurrence of a closed substring that cannot be extended to the left nor to the right into a longer closed substring. MCSs with exponent at least 2 are commonly called runs; those with exponent smaller than 2, instead, are particular cases of maximal gapped repeats. We show that a string of length n contains O(n 1.5 ) MCSs. We also provide an output-sensitive algorithm that, given a string of length n over a constant-size alphabet, locates all m MCSs the string contains in O(n log n + m) time.

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Tighter Bounds and Optimal Algorithms for All Maximal α-gapped Repeats and Palindromes

Cited by 20 publications

References 20 publications

Almost Optimal Searching of Maximal Subrepetitions in a Word

Almost Optimal Searching of Maximal Subrepetitions in a Word

Computing palindromes and suffix trees of dynamic trees

Maximal Closed Substrings

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