NDLI: More Time-Space Tradeoffs for Finding a Shortest Unique Substring

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More Time-Space Tradeoffs for Finding a Shortest Unique Substring

Content Provider	MDPI
Author	Bannai, Hideo Gagie, Travis Hoppenworth, Gary Puglisi, Simon J. Russo, Luís M. S.
Copyright Year	2020
Abstract	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 $O (n (L / m) {log}^{2} (L) log log σ)$ time using $O ((L / m) {log}^{2} L)$ sequential passes over T. We then describe how, for constant k, with high probability, we can find a k-mismatch SUS in $O (n^{1 + ϵ} L / m)$ time using $O (n^{ϵ} L / m)$ sequential passes over T, again using only m words of workspace. Finally, we also describe a deterministic algorithm that takes $O (n τ log σ log n)$ time to find an SUS using $O (n / τ)$ words of workspace, where $τ$ is a parameter.
Starting Page	234
e-ISSN	19994893
DOI	10.3390/a13090234
Journal	Algorithms
Issue Number	9
Volume Number	13
Language	English
Publisher	MDPI
Publisher Date	2020-09-18
Access Restriction	Open
Subject Keyword	Algorithms Robotics Shortest Unique Substring K-mismatch Sus Time-space Tradeoff Karp–rabin Sketching Suffix Trees
Content Type	Text
Resource Type	Article

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