Shortest Unique Palindromic Substring Queries on Run-Length Encoded Strings

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

doi:10.1007/978-3-030-25005-8_35

Cited by 5 publications

(2 citation statements)

References 12 publications

(34 reference statements)

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“…The authors gave an O(n 2 )-time and O(n)-space algorithm, which finds the shortest unique substring covering every position of T. Since then, the problem has been revisited and optimal O(n)-time algorithms have been presented by Ileri et al [8] and Tsuruta et al [9]. Several other variants of this problem have been investigated [10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Efficient Data Structures for Range Shortest Unique Substring Queries

et al. 2020

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Let T[1,n] be a string of length n and T[i,j] be the substring of T starting at position i and ending at position j. A substring T[i,j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α,β], return a shortest substring T[i,j] of T with exactly one occurrence in [α,β]. We present an O(nlogn)-word data structure with O(logwn) query time, where w=Ω(logn) is the word size. Our construction is based on a non-trivial reduction allowing for us to apply a recently introduced optimal geometric data structure [Chan et al., ICALP 2018]. Additionally, we present an O(n)-word data structure with O(nlogϵn) query time, where ϵ>0 is an arbitrarily small constant. The latter data structure relies heavily on another geometric data structure [Nekrich and Navarro, SWAT 2012].

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Section: Introductionmentioning

confidence: 99%

Efficient Data Structures for Range Shortest Unique Substring Queries

et al. 2020

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“…The authors gave an O(n 2 )-time and O(n)-space algorithm, which finds the shortest unique substring covering every position of T. Since then, the problem has been revisited and optimal O(n)-time algorithms have been presented by Ileri et al [16] and by Tsuruta et al [27]. Several other variants of this problem have been investigated [2,10,11,15,18,20,21,24,28].…”

Section: Introductionmentioning

confidence: 99%

Range Shortest Unique Substring Queries

Abedin

Ganguly

Pissis

et al. 2019

String Processing and Information Retrieval

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Let T[1, n] be a string of length n and T[i, j] be the substring of T starting at position i and ending at position j. A substring T[i, j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and in information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α, β], return a shortest substring T[i, j] of T with exactly one occurrence in [α, β]. We present an O(n log n)-word data structure with O(log w n) query time, where w = Ω(log n) is the word size. Our construction is based on a non-trivial reduction allowing us to apply a recently introduced optimal geometric data structure [Chan et al. ICALP 2018].

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