Compact Data Structures for Shortest Unique Substring Queries

Mieno, Takuya; Köppl, Dominik; Nakashima, Yuto; Inenaga, Shunsuke; Bannai, Hideo; Takeda, Masayuki

doi:10.1007/978-3-030-32686-9_8

Cited by 5 publications

(3 citation statements)

References 14 publications

(34 reference statements)

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“…Although not mentioned explicitly in [16], the size of their data structure (except for the input string) and query time can be respectively written as O(m) space and O( √ log m∕ log log m + occ) time with respect to the number m of MUSs of the input string T. Note that all the above algorithms for the SUS problems compute all MUSs of the given string (or some data structure which is essentially equivalent to MUSs) in the preprocessing. We also refer to [1,3,7,17] for related results on the SUS problems.…”

Section: Minimal Unique Substrings and Shortest Unique Substringsmentioning

confidence: 99%

Computing Minimal Unique Substrings for a Sliding Window

et al. 2021

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A substring u of a string T is called a minimal unique substring (MUS) of T if u occurs exactly once in T and any proper substring of u occurs at least twice in T. In this paper, we study the problem of computing MUSs for a sliding window over a given string T. We first show how the set of MUSs can change when the window slides over T. We then present an $$O(n\log \sigma ')$$ O ( n log σ ′ ) -time and O(d)-space algorithm to compute MUSs for a sliding window of size d over the input string T of length n, where $$\sigma '\le d$$ σ ′ ≤ d is the maximum number of distinct characters in every window.

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Section: Minimal Unique Substrings and Shortest Unique Substringsmentioning

confidence: 99%

Computing Minimal Unique Substrings for a Sliding Window

et al. 2021

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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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“…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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Compact Data Structures for Shortest Unique Substring Queries

Cited by 5 publications

References 14 publications

Computing Minimal Unique Substrings for a Sliding Window

Computing Minimal Unique Substrings for a Sliding Window

Efficient Data Structures for Range Shortest Unique Substring Queries

Range Shortest Unique Substring Queries

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