A simple yet time-optimal and linear-space algorithm for shortest unique substring queries

İleri, Atalay Mert; Külekçi, M. Oğuzhan; Xu, Bojian

doi:10.1016/j.tcs.2014.11.004

Cited by 16 publications

(15 citation statements)

References 6 publications

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“…It is worth noting that our solution does not involve any compressed or succinct data structures, making our solution practical and easy to implement. Our preliminary experimental study shows that our solution for exact SUS finding is even faster than the fastest one among [7,8,5] 5 , in addition to a lot more space saving than them, enabling our solution to handle larger data sets. Due to page limit, we will deliver the details of our experimental study in the journal version of this paper.…”

Section: Prior Work and Our Contributionmentioning

confidence: 99%

“…(2) It needs another n bytes to save the original string S in order to output the actual content of any SUS of interest from queries. Note that all prior work [7,8,5,4] use O(n) space but there is big leading constant hidden within the big-oh notation (see the experimental study in [5]). -After the suffix array is constructed, all the computation in our solution happens in the place of two integer arrays, using non-trivial techniques.…”

Section: Prior Work and Our Contributionmentioning

confidence: 99%

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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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Section: Prior Work and Our Contributionmentioning

confidence: 99%

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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“…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%

“…Their data structure can be constructed in O(n) time. İleri et al [9] independently showed another data structure with the same time complexities. For the general point SUS problem, Tsuruta et al [19] can also resort to their proposed data structure returning all SUSs for a query position in optimal O(occ) time, where occ is the number of returned SUSs.…”

Section: Introductionmentioning

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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“…In addition to the related work discussed in Section I, there were recently a sequence of work on finding shortest unique substrings (SUS) [15], [16], [17], [18], [1], of which Hu et al [1] studied the generalized version of SUS finding: Given a string position interval [x..y], 1 ≤ x ≤ y ≤ n, find SUS y x , the shortest unique substring that covers the string position interval [x..y], or the fact that such SUS y x does not exist. To the best of our knowledge, no efficient reduction from LR finding to SUS finding is known as of now.…”

Section: Prior Work and Our Contributionmentioning

confidence: 99%

On stabbing queries for generalized longest repeat

2015

2015 IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

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A longest repeat query on a string, motivated by its applications in many subfields including computational biology, asks for the longest repetitive substring(s) covering a particular string position (point query). In this paper, we extend the longest repeat query from point query to interval query, allowing the search for longest repeat(s) covering any position interval, and thus significantly improve the usability of the solution. Our method for interval query takes a different approach using the insight from a recent work on shortest unique substrings [1], as the prior work's approach for point query becomes infeasible in the setting of interval query. Using the critical insight from [1], we propose an indexing structure, which can be constructed in the optimal O(n) time and space for a string of size n, such that any future interval query can be answered in O(1) time. Further, our solution can find all longest repeats covering any given interval using optimal O(occ) time, where occ is the number of longest repeats covering that given interval, whereas the prior O(n)-time and space work can find only one candidate for each point query. Experiments with real-world biological data show that our proposal is competitive with prior works, both time and space wise, while providing with the new functionality of interval queries as opposed to point queries provided by prior works.

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A simple yet time-optimal and linear-space algorithm for shortest unique substring queries

Cited by 16 publications

References 6 publications

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

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

Compact Data Structures for Shortest Unique Substring Queries

On stabbing queries for generalized longest repeat

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