Shortest Unique Queries on Strings

Hu, Xiaocheng; Pei, Jian; Tao, Yufei

doi:10.1007/978-3-319-11918-2_16

Cited by 25 publications

(42 citation statements)

References 9 publications

(12 reference statements)

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“…We use the following two sets containing interval and point SUSs, which were defined at the beginning of the introduction: Given an interval [s, t] ⊂ [1, n], [4,5], [5,8], [6,9], [7,11], [10,12], [13,14] [6,9], and rmMUS p T = [6,9].…”

Section: Muss and Sussmentioning

confidence: 99%

Compact Data Structures for Shortest Unique Substring Queries

Mieno

Köppl

Nakashima

et al. 2019

String Processing and Information Retrieval

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Given a string T of length n, a substring u = T [i..j] of T is called a shortest unique substring (SUS) for an interval [s, t] if (a) u occurs exactly once in T , (b) u contains the interval [s, t] (i.e. i ≤ s ≤ t ≤ j), and (c) every substring v of T with |v| < |u| containing [s, t] occurs at least twice in T . Given a query interval [s, t] ⊂ [1, n], the interval SUS problem is to output all the SUSs for the interval [s, t].In this article, we propose a 4n+o(n) bits data structure answering an interval SUS query in output-sensitive O(occ) time, where occ is the number of returned SUSs. Additionally, we focus on the point SUS problem, which is the interval SUS problem for s = t. Here, we propose a ⌈(log 2 3 + 1)n⌉ + o(n) bits data structure answering a point SUS query in the same output-sensitive time.

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Section: Muss and Sussmentioning

confidence: 99%

Compact Data Structures for Shortest Unique Substring Queries

Mieno

Köppl

Nakashima

et al. 2019

String Processing and Information Retrieval

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“…Let S = acbaaabcbcbcbaab. SUPS for interval [6,7] is the S[3..7] = baaab. SUPS for interval [7,8] In this paper, we tackle the following problem.…”

Section: Mups S Sups S and Our Problemmentioning

confidence: 99%

Shortest Unique Palindromic Substring Queries in Optimal Time

Nakashima

Inoue

Mieno

et al. 2018

Lecture Notes in Computer Science

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A palindrome is a string that reads the same forward and backward. A palindromic substring P of a string S is called a shortest unique palindromic substring (SUPS ) for an interval [s, t] in S, if P occurs exactly once in S, this occurrence of P contains interval [s, t], and every palindromic substring of S which contains interval [s, t] and is shorter than P occurs at least twice in S. The SUPS problem is, given a string S, to preprocess S so that for any subsequent query interval [s, t] all the SUPS s for interval [s, t] can be answered quickly. We present an optimal solution to this problem. Namely, we show how to preprocess a given string S of length n in O(n) time and space so that all SUPS s for any subsequent query interval can be answered in O(α + 1) time, where α is the number of outputs.

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“…Following their proposal, there has been a sequence of improvements [8,5] for exact SUS finding, reducing the time cost from O(n 2 ) to O(n) and alleviating the underlying data structure from suffix tree to suffix array of O(n) space. Hu et al [4] proposed an RMQ (range minimum query) technique based indexing structure, which can be constructed in O(n) time and space, such that any future exact SUS covering any interval of string positions can be answered in O(1) time. In this work, we make the following contributions:…”

Section: Prior Work and Our Contributionmentioning

confidence: 99%

An In-place Framework for Exact and Approximate Shortest Unique Substring Queries

Hon

Thankachan

2015

Algorithms and Computation

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Abstract. We revisit the exact shortest unique substring (SUS) finding problem, and propose its approximate version where mismatches are allowed, due to its applications in subfields such as computational biology. We design a generic in-place framework that fits to solve both the exact and approximate k-mismatch SUS finding, using the minimum 2n memory words plus n bytes space, where n is the input string size. By using the in-place framework, we can find the exact and approximate k-mismatch SUS for every string position using a total of O(n) and O(n 2 ) time, respectively, regardless of the value of k. Our framework does not involve any compressed or succinct data structures and thus is practical and easy to implement.

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Shortest Unique Queries on Strings

Cited by 25 publications

References 9 publications

Compact Data Structures for Shortest Unique Substring Queries

Compact Data Structures for Shortest Unique Substring Queries

Shortest Unique Palindromic Substring Queries in Optimal Time

An In-place Framework for Exact and Approximate Shortest Unique Substring Queries

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