Computing longest palindromic substring after single-character or block-wise edits

Funakoshi, Mitsuru; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki

doi:10.1016/j.tcs.2021.01.014

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…Afterward, Abedin et al [1] improved the complexities. Also, the problems of computing the longest Lyndon substring [29], the longest palindrome [15], and the set of MUPSs [14] were considered in the after-edit model.…”

Section: Related Workmentioning

confidence: 99%

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%

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Mieno¹,

Funakoshi²

2022

Preprint

Self Cite

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“…They proposed an algorithm that computes the longest common factor of two strings after a single-character edit operation, i.e., insertion, deletion, and substitution. Also, there are several studies of the same settings for some notions of regularities of strings [22,1,10]. In particular, regarding palindromic structures, Funakoshi et al [10] proposed algorithms for computing the longest palindromic substring after single-character or block-wise edit operations.…”

Section: Related Workmentioning

confidence: 99%

“…Also, there are several studies of the same settings for some notions of regularities of strings [22,1,10]. In particular, regarding palindromic structures, Funakoshi et al [10] proposed algorithms for computing the longest palindromic substring after single-character or block-wise edit operations.…”

Section: Related Workmentioning

confidence: 99%

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Minimal unique palindromic substrings after single-character substitution

Funakoshi¹,

Mieno²

2021

Preprint

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A palindrome is a string that reads the same forward and backward. A palindromic substring w of a string T is called a minimal unique palindromic substring (MUPS ) of T if w occurs only once in T and any proper palindromic substring of w occurs at least twice in T . MUPSs are utilized for answering the shortest unique palindromic substring problem, which is motivated by molecular biology [Inoue et al., 2018]. Given a string T of length n, all MUPSs of T can be computed in O(n) time. In this paper, we study the problem of updating the set of MUPSs when a character in the input string T is substituted by another character. We first analyze the number d of changes of MUPSs when a character is substituted, and show that d is in O(log n). Further, we present an algorithm that uses O(n) time and space for preprocessing, and updates the set of MUPSs in O(log σ + (log log n) 2 + d) time where σ is the alphabet size. We also propose a variant of the algorithm, which runs in optimal O(d) time when the alphabet size is constant.

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“…Regarding longest palindrome computation, Funakoshi et al [18] considered the problem of computing the longest palindromic substring of the string T after a single character insertion, deletion, or substitution is applied to the input string T of length n. Of course, using O(n) time, we can obtain the longest palindromic substring of T from scratch. The idea is too naïve and looks inefficient.…”

Section: Introductionmentioning

confidence: 99%

Internal Longest Palindrome Queries in Optimal Time

Mitani¹,

Mieno²,

Seto³

et al. 2022

Preprint

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Palindromes are strings that read the same forward and backward. Problems of computing palindromic structures in strings have been studied for many years with a motivation of their application to biology. The longest palindrome problem is one of the most important and classical problems regarding palindromic structures, that is, to compute the longest palindrome appearing in a string T of length n. The problem can be solved in O(n) time by the famous algorithm of Manacher [Journal of the ACM, 1975]. In this paper, we consider the problem in the internal model. The internal longest palindrome query is, given a substring T [i..j] of T as a query, to compute the longest palindrome appearing in T [i..j]. The best known data structure for this problem is the one proposed by Amir et al. [Algorithmica, 2020], which can answer any query in O(log n) time. In this paper, we propose a linear-size data structure that can answer any internal longest palindrome query in constant time. Also, given the input string T , our data structure can be constructed in O(n) time.

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Computing longest palindromic substring after single-character or block-wise edits

Cited by 10 publications

References 17 publications

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Minimal unique palindromic substrings after single-character substitution

Internal Longest Palindrome Queries in Optimal Time

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