A Linear Time Algorithm for Seeds Computation

Kociumaka, Tomasz; Kubica, Marcin; Radoszewski, Jakub; Rytter, Wojciech; Waleń, Tomasz

doi:10.1137/1.9781611973099.86

Cited by 27 publications

(31 citation statements)

References 34 publications

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“…We considered the generalized on-line variant of the longest common property preserved substring problem proposed by Ayad et al [1,16], and 1) unified the two problem settings, and 2) proposed algorithms for several properties, namely, squares, periodic substrings, palindromes, and Lyndon words. For all these properties, we can answer queries in O(|y| log σ) time and O(1) working space, with O(n) time and space preprocessing.…”

Section: Resultsmentioning

confidence: 99%

On Longest Common Property Preserved Substring Queries

Kai

Nakashima

Inenaga

et al. 2019

String Processing and Information Retrieval

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We revisit the problem of longest common property preserving substring queries introduced by Ayad et al. (SPIRE 2018, arXiv 2018. We consider a generalized and unified on-line setting, where we are given a set X of k strings of total length n that can be pre-processed so that, given a query string y and a positive integer k ≤ k, we can determine the longest substring of y that satisfies some specific property and is common to at least k strings in X. Ayad et al. considered the longest square-free substring in an on-line setting and the longest periodic and palindromic substring in an off-line setting. In this paper, we give efficient solutions in the on-line setting for finding the longest common square, periodic, palindromic, and Lyndon substrings. More precisely, we show that X can be pre-processed in O(n) time resulting in a data structure of O(n) size that answers queries in O(|y| log σ) time and O(1) working space, where σ is the size of the alphabet, and the common substring must be a square, a periodic substring, a palindrome, or a Lyndon word.

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Section: Resultsmentioning

confidence: 99%

On Longest Common Property Preserved Substring Queries

Kai

Nakashima

Inenaga

et al. 2019

String Processing and Information Retrieval

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“…2. Furthermore, s is called a left seed of w if s is both a prefix and a seed of w. Thus a cover of w is always a left seed of w, and a left seed of w is a seed of w. The notion of seed was introduced in [5] and efficient computation of seeds was further considered in [3,6]. In the proof of our main result we use the following easy observations that are immediate consequences of the definitions of cover and seed.…”

Section: Preliminariesmentioning

confidence: 99%

Two strings at Hamming distance 1 cannot be both quasiperiodic

Amir

Iliopoulos

Radoszewski

2017

Information Processing Letters

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We present a generalization of a known fact from combinatorics on words related to periodicity into quasiperiodicity. A string is called periodic if it has a period which is at most half of its length. A string w is called quasiperiodic if it has a non-trivial cover, that is, there exists a string c that is shorter than w and such that every position in w is inside one of the occurrences of c in w. It is a folklore fact that two strings that differ at exactly one position cannot be both periodic. Here we prove a more general fact that two strings that differ at exactly one position cannot be both quasiperiodic. Along the way we obtain new insights into combinatorics of quasiperiodicities.

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“…We will show that given CST (w) and CST (w R ) we can compute the representation of all seeds from Lemma 6 in O(n) time. Let us recall auxiliary notions of quasiseed and quasigap, see [19].…”

Section: By-products Of Cover Suffix Treementioning

confidence: 99%

Fast Algorithm for Partial Covers in Words

et al. 2014

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A factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w. A word w covered by u thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of u. In this article we introduce a new notion of α-partial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least α positions in w. We develop a data structure of O(n) size (where n = |w|) that can be constructed in O(n log n) time which we apply to compute all shortest α-partial covers for a given α. We also employ it for an O(n log n)-time algorithm computing a shortest α-partial cover for each α = 1, 2, . . . , n.Keywords Cover of a word · Quasiperiodicity · Suffix tree

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A Linear Time Algorithm for Seeds Computation

Cited by 27 publications

References 34 publications

On Longest Common Property Preserved Substring Queries

On Longest Common Property Preserved Substring Queries

Two strings at Hamming distance 1 cannot be both quasiperiodic

Fast Algorithm for Partial Covers in Words

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