Fast Algorithms for the Shortest Unique Palindromic Substring Problem on Run-Length Encoded Strings

Watanabe, Kiichi; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki

doi:10.1007/s00224-020-09980-x

Cited by 9 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we propose space-efficient SUPS data structures. As related work, Watanabe et al [34] proposed a SUPS data structure of size O(r) where r ≤ n is the size of the run-length encoded string. Their data structure will be small when the input string is highly compressible with run-length encoding.…”

Section: Compact Sups Data Structuresmentioning

confidence: 99%

“…The (interval) SUPS problem was formalized by Inoue et al [22], and they showed that all SUPSs for a query interval can be enumerated in O(α) time after O(n)-time preprocessing, where α is the number of SUPSs to output. Watanabe et al [34] considered the SUPS problem on run-length encoded strings to reduce the space usage. They proposed an O(r)-space data structure that can enumerate all SUPSs for a query interval in O( log r/ log log r + α) time where r is the size of the run-length encoded string, which satisfies r ≤ n.…”

Section: Introductionmentioning

confidence: 99%

“…{[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.…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Mieno,

Funakoshi

2023

Algorithmica

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 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.

show abstract

Section: Compact Sups Data Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Mieno,

Funakoshi

2023

Algorithmica

View full text Add to dashboard Cite

show abstract

“…The SUPS problem was formalized by Inoue et al [19], and they showed that all SUPSs for a query interval can be enumerated in O(α) time after O(n)-time preprocessing, where α is the number of SUPSs to output. Watanabe et al [30] considered the SUPS problem on run-length encoded strings and showed that all SUPSs for a query can be enumerated in O( log r/ log log r + α) time after O(r log σ R + r log r/ log log r) time preprocessing, where r is the size of the run-length encoded string and σ R is the number of distinct runs in the input.…”

Section: Introductionmentioning

confidence: 99%

Shortest Unique Palindromic Substring Queries in Semi-dynamic Settings

Mieno¹,

Funakoshi²

2022

Preprint

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. 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

“…They showed that there are no more than n MUPSs in any length-n string, and proposed an O(n)-time algorithm to compute all MUPSs of a given string of length n over an integer alphabet of size n O (1) . After that, Watanabe et al [23] considered the problem of computing MUPSs in an run-length encoded (RLE ) string. They showed that there are no more than m MUPSs in a string whose RLE size is m. Also, they proposed an O(m log σ R )-time and O(m)-space algorithm to compute all MUPSs of a string given in RLE, where m is the RLE size of the string, and σ R is the number of distinct single-character runs in the RLE string.…”

Section: Introductionmentioning

confidence: 99%

Minimal unique palindromic substrings after single-character substitution

Funakoshi¹,

Mieno²

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

Fast Algorithms for the Shortest Unique Palindromic Substring Problem on Run-Length Encoded Strings

Cited by 9 publications

References 14 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

Minimal unique palindromic substrings after single-character substitution

Contact Info

Product

Resources

About