TY - JOUR

T1 - More time-space tradeoffs for finding a shortest unique substring

AU - Bannai, Hideo

AU - Gagie, Travis

AU - Hoppenworth, Gary

AU - Puglisi, Simon J.

AU - Russo, Luís M.S.

N1 - Funding Information:
Funding: H.B. was partially funded by JSPS KAKENHI Grant Numbers JP16H02783, JP20H04141. T.G. was partially funded by NSERC grant RGPIN-07185-2020. S.J.P. was partially supported by Academy of Finland grant 319454. L.M.S.R. was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with reference UIDB/50021/2020. This paper resulted from a meeting at INESC in 2017 funded by the EU’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement No 690941 (BIRDS).

PY - 2020/9

Y1 - 2020/9

N2 - We extend recent results regarding finding shortest unique substrings (SUSs) to obtain new time-space tradeoffs for this problem and the generalization of finding k-mismatch SUSs. Our new results include the first algorithm for finding a k-mismatch SUS in sublinear space, which we obtain by extending an algorithm by Senanayaka (2019) and combining it with a result on sketching by Gawrychowski and Starikovskaya (2019). We first describe how, given a text T of length n and m words of workspace, with high probability we can find an SUS of length L in O(n(L/m) log L) time using random access to T, or in O(n(L/m) log2(L) log log σ) time using O((L/m) log2 L) sequential passes over T. We then describe how, for constant k, with high probability, we can find a k-mismatch SUS in O(n1+eL/m) time using O(neL/m) sequential passes over T, again using only m words of workspace. Finally, we also describe a deterministic algorithm that takes O(nτ log σ log n) time to find an SUS using O(n/τ) words of workspace, where τ is a parameter.

AB - We extend recent results regarding finding shortest unique substrings (SUSs) to obtain new time-space tradeoffs for this problem and the generalization of finding k-mismatch SUSs. Our new results include the first algorithm for finding a k-mismatch SUS in sublinear space, which we obtain by extending an algorithm by Senanayaka (2019) and combining it with a result on sketching by Gawrychowski and Starikovskaya (2019). We first describe how, given a text T of length n and m words of workspace, with high probability we can find an SUS of length L in O(n(L/m) log L) time using random access to T, or in O(n(L/m) log2(L) log log σ) time using O((L/m) log2 L) sequential passes over T. We then describe how, for constant k, with high probability, we can find a k-mismatch SUS in O(n1+eL/m) time using O(neL/m) sequential passes over T, again using only m words of workspace. Finally, we also describe a deterministic algorithm that takes O(nτ log σ log n) time to find an SUS using O(n/τ) words of workspace, where τ is a parameter.

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U2 - 10.3390/A13090234

DO - 10.3390/A13090234

M3 - Article

AN - SCOPUS:85091918586

VL - 13

JO - Algorithms

JF - Algorithms

SN - 1999-4893

IS - 9

M1 - 234

ER -