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Dynamic Suffix Array with Polylogarithmic Queries and Updates ...
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Breaking the $O(n)$-Barrier in the Construction of Compressed Suffix Arrays ...
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Time-Space Tradeoffs for Finding a Long Common Substring ...
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Time-Space Tradeoffs for Finding a Long Common Substring ...
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Abstract:
We consider the problem of finding, given two documents of total length n, a longest string occurring as a substring of both documents. This problem, known as the Longest Common Substring (LCS) problem, has a classic 𝒪(n)-time solution dating back to the discovery of suffix trees (Weiner, 1973) and their efficient construction for integer alphabets (Farach-Colton, 1997). However, these solutions require Θ(n) space, which is prohibitive in many applications. To address this issue, Starikovskaya and Vildhøj (CPM 2013) showed that for n^{2/3} ≤ s ≤ n, the LCS problem can be solved in 𝒪(s) space and 𝒪̃(n²/s) time. Kociumaka et al. (ESA 2014) generalized this tradeoff to 1 ≤ s ≤ n, thus providing a smooth time-space tradeoff from constant to linear space. In this paper, we obtain a significant speed-up for instances where the length L of the sought LCS is large. For 1 ≤ s ≤ n, we show that the LCS problem can be solved in 𝒪(s) space and 𝒪̃(n²/(L⋅s) +n) time. The result is based on techniques originating from the ... : LIPIcs, Vol. 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020), pages 5:1-5:14 ...
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Keyword:
local consistency; longest common substring; periodicity; time-space tradeoff
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URL: https://dx.doi.org/10.4230/lipics.cpm.2020.5 https://drops.dagstuhl.de/opus/volltexte/2020/12130/
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Practical Performance of Space Efficient Data Structures for Longest Common Extensions ...
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Longest Unbordered Factor in Quasilinear Time
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Kociumaka, Tomasz; Kundu, Ritu; Mohamed, Manal. - : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018. : LIPIcs - Leibniz International Proceedings in Informatics. 29th International Symposium on Algorithms and Computation (ISAAC 2018), 2018
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Efficient Index for Weighted Sequences
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Barton, Carl; Kociumaka, Tomasz; Pissis, Solon P.. - : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. : LIPIcs - Leibniz International Proceedings in Informatics. 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016), 2016
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Minimal Suffix and Rotation of a Substring in Optimal Time
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Kociumaka, Tomasz. - : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. : LIPIcs - Leibniz International Proceedings in Informatics. 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016), 2016
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Minimal Suffix and Rotation of a Substring in Optimal Time ...
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Kociumaka, Tomasz. - : Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany, 2016
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Sparse Suffix Tree Construction in Optimal Time and Space ...
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Minimal Suffix and Rotation of a Substring in Optimal Time ...
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