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:
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 Funda??o para a Ci?ncia 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 Sk?odowska-Curie grant agreement No 690941 (BIRDS).The authors are very grateful to Tatiana Starikovskaya and Sharma Thankachan for helpful discussions. The second author is also grateful to Starikovskaya for once saving him from a wild boar.
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).
Publisher Copyright:
© 2020 by the authors.

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.

UR - http://www.scopus.com/inward/record.url?scp=85091918586&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85091918586&partnerID=8YFLogxK

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 -