Repetition Detection in a Dynamic String

Amir, Amihood; Boneh, Itai; Charalampopoulos, Panagiotis; Kondratovsky, Eitan

doi:10.4230/lipics.esa.2019.5

Cited by 12 publications

(7 citation statements)

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“…They also developed a general (probabilistic) scheme for dynamic problems on strings and applied it to the computation of the longest Lyndon substring and the longest palindrome in a dynamic string. Besides that, there are several studies for dynamic settings (e.g., [16,4,8]). In particular, a fully-dynamic and deterministic algorithm for computing the longest palindrome was shown in [3].…”

Section: Related Workmentioning

confidence: 99%

“…The operator + denotes the concatenation of strings. For this string and query interval [18,18] (highlighted in blue in the figure), SUPS S ( [18,18]) = { [1,19], [4,22], [16,34], [18,36]} holds. Note that palindromes S[2..18], S [5..21], and S [17..33], which are shorter than 19 and cover the interval [18,18], are not unique since each of them has another occurrence in the artificial gadgets concatenated by + operators.…”

Section: Tight Bounds On Maximum Number Of Supss For Single Querymentioning

confidence: 99%

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Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Mieno¹,

Funakoshi²

2022

Preprint

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A palindromic substring T [i..j] of a string T is said to be a shortest unique palindromic substring (SUPS) in T for an interval [p, q] if T [i..j] is a shortest one such that T [i..j] occurs only once in T , and [i, j] contains [p, q]. The SUPS problem is, given a string T of length n, to construct a data structure that can compute all the SUPSs for any given query interval. It is known that any SUPS query can be answered in O(α) time after O(n)-time preprocessing, where α is the number of SUPSs to output [Inoue et al., 2018]. In this paper, we first show that α is at most 4, and the upper bound is tight. Also, we present an algorithm to solve the SUPS problem for a sliding window that can answer any query in O(log log W ) time and update data structures in amortized O(log σ) time, where W is the size of the window, and σ is the alphabet size. Furthermore, we consider the SUPS problem in the after-edit model and present an efficient algorithm. Namely, we present an algorithm that uses O(n) time for preprocessing and answers any k SUPS queries in O(log n log log n + k log log n) time after single character substitution. As a by-product, we propose a fully-dynamic data structure for range minimum queries (RmQs) with a constraint where the width of each query range is limited to polylogarithmic. The constrained RmQ data structure can answer such a query in constant time and support a single-element edit operation in amortized constant time.

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Section: Related Workmentioning

confidence: 99%

Section: Tight Bounds On Maximum Number Of Supss For Single Querymentioning

confidence: 99%

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Mieno¹,

Funakoshi²

2022

Preprint

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“…There are O(n log n)-time algorithms for finding all the square substrings of the input string [Cro81, ML84, AIP87]. There are data structures [ABCK19] for dynamically maintaining the longest square substring under character substitutions.…”

Section: Related Workmentioning

confidence: 99%

Near-Optimal Quantum Algorithms for String Problems

Akmal¹,

Jin²

2021

Preprint

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We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology literature since the 1970s, and are known to be solvable by near-linear time classical algorithms. In this work, we give quantum algorithms for these problems with near-optimal query complexities and time complexities. Specifically, we show that:• Longest Common Substring can be solved by a quantum algorithm in Õ(n 2/3 ) time, improving upon the recent Õ(n 5/6 )-time algorithm by Le Gall and Seddighin (2020). Our algorithm uses the MNRS quantum walk framework, together with a careful combination of string synchronizing sets (Kempa and Kociumaka, 2019) and generalized difference covers.• Lexicographically Minimal String Rotation can be solved by a quantum algorithm in n 1/2+o(1) time, improving upon the recent Õ(n 3/4 )-time algorithm by Wang and Ying (2020). We design our algorithm by first giving a new classical divide-and-conquer algorithm in near-linear time based on exclusion rules, and then speeding it up quadratically using nested Grover search and quantum minimum finding.• Longest Square Substring can be solved by a quantum algorithm in Õ( √ n) time. Our algorithm is an adaptation of the algorithm by Le Gall and Seddighin (2020) for the Longest Palindromic Substring problem, but uses additional techniques to overcome the difficulty that binary search no longer applies.Our techniques naturally extend to other related string problems, such as Longest Repeated Substring, Longest Lyndon Substring, and Minimal Suffix.

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“…Efficient algorithms for approximate pattern matching in the dynamic setting were recently presented in [10]. Other problems on strings that have been studied in the dynamic setting include maintaining repetitions, such as the set of square substrings [5] or a longest palindromic substring [4,7].…”

Section: Problem: Longest Common Substringmentioning

confidence: 99%

Dynamic Longest Common Substring in Polylogarithmic Time

Charalampopoulos,

Gawrychowski,

Pokorski

2020

Preprint

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The longest common substring problem consists in finding a longest string that appears as a (contiguous) substring of two input strings. We consider the dynamic variant of this problem, in which we are to maintain two dynamic strings S and T , each of length at most n, that undergo substitutions of letters, in order to be able to return a longest common substring after each substitution. Recently, Amir et al. [ESA 2019] presented a solution for this problem that needs only Õ(n 2/3 ) time per update. This brought the challenge of determining whether there exists a faster solution with polylogarithmic update time, or (as is the case for other dynamic problems), we should expect a polynomial (conditional) lower bound. We answer this question by designing a significantly faster algorithm that processes each substitution in amortized log O(1) n time with high probability. Our solution relies on exploiting the local consistency of the parsing of a collection of dynamic strings due to Gawrychowski et al. [SODA 2018], and on maintaining two dynamic trees with labeled bicolored leaves, so that after each update we can report a pair of nodes, one from each tree, of maximum combined weight, which have at least one common leaf-descendant of each color. We complement this with a lower bound of Ω(log n/ log log n) for the update time of any polynomial-size data structure that maintains the LCS of two dynamic strings, and the same lower bound for the update time of any data structure of size Õ(n) that maintains the LCS of a static and a dynamic string. Both lower bounds hold even allowing amortization and randomization.

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Repetition Detection in a Dynamic String

Cited by 12 publications

References 0 publications

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Near-Optimal Quantum Algorithms for String Problems

Dynamic Longest Common Substring in Polylogarithmic Time

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