Computing Minimal Unique Substrings for a Sliding Window

Mieno, Takuya; Fujishige, Yuta; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki

doi:10.1007/s00453-021-00864-1

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…The sliding-window LZ77 compression is based on the sliding-window suffix tree [13,25,30,32]. Also, the sliding-window suffix tree can be applied to compute minimal absent words [11] and minimal unique substrings [28], which are significant concepts for bioinformatics, in the slidingwindow model. Recently, the sliding-window palindromic tree was proposed, and it can be applied to compute MUPSs in the sliding-window model [29].…”

Section: Related Workmentioning

confidence: 99%

Data Structures for Computing Unique Palindromes in Static and Non-Static Strings

Mieno,

Funakoshi

2023

Algorithmica

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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.We also show that the total sum of lengths of minimal unique substrings of string T , which is strongly related to SUPSs, is O(n). Then, we present the first O(n)-bits data structures that can answer any SUPS query in constant time. 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 Data structures for computing unique palindromes in (non-)static strings in O(log n log log n + k log log n) time after single character substitution. Finally, 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 poly-logarithmic. 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%

Data Structures for Computing Unique Palindromes in Static and Non-Static Strings

Mieno,

Funakoshi

2023

Algorithmica

Self Cite

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show abstract

“…The sliding-window LZ77 compression is based on the sliding-window suffix tree [12,22,28,27]. Also, the sliding-window suffix tree can be applied to compute minimal absent words [10] and minimal unique substrings [24], which are significant concepts for bioinformatics, in the sliding-window model. Recently, the sliding-window palindromic tree was proposed, and it can be applied to compute MUPSs in the slidingwindow model [25].…”

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.

show abstract

Section: Related Workmentioning

confidence: 99%

Data structures for computing unique palindromes in static and non-static strings

Mieno

Funakoshi

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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. We also show that the total sum of lengths of minimal unique substrings of string T, which is strongly related to SUPSs, is O(n). Then, we present the first O(n)-bits data structures that can answer any SUPS query in constant time. 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. Finally, 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 poly-logarithmic. The constrained RmQ data structure can answer such a query in constant time and support a single-element edit operation in amortized constant time.

show abstract

Computing Minimal Unique Substrings for a Sliding Window

Cited by 4 publications

References 22 publications

Data Structures for Computing Unique Palindromes in Static and Non-Static Strings

Data Structures for Computing Unique Palindromes in Static and Non-Static Strings

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Data structures for computing unique palindromes in static and non-static strings

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