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Constructing Strings Avoiding Forbidden Substrings
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In: CPM 2021 - 32nd Annual Symposium on Combinatorial Pattern Matching ; https://hal.inria.fr/hal-03395386 ; CPM 2021 - 32nd Annual Symposium on Combinatorial Pattern Matching, Jul 2021, Wroclaw, Poland. pp.1-18 (2021)
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Faster Algorithms for Longest Common Substring ...
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Abstract:
In the classic longest common substring (LCS) problem, we are given two strings S and T, each of length at most n, over an alphabet of size σ, and we are asked to find a longest string occurring as a fragment of both S and T. Weiner, in his seminal paper that introduced the suffix tree, presented an 𝒪(n log σ)-time algorithm for this problem [SWAT 1973]. For polynomially-bounded integer alphabets, the linear-time construction of suffix trees by Farach yielded an 𝒪(n)-time algorithm for the LCS problem [FOCS 1997]. However, for small alphabets, this is not necessarily optimal for the LCS problem in the word RAM model of computation, in which the strings can be stored in 𝒪(n log σ/log n) space and read in 𝒪(n log σ/log n) time. We show that, in this model, we can compute an LCS in time 𝒪(n log σ / √{log n}), which is sublinear in n if σ = 2^{o(√{log n})} (in particular, if σ = 𝒪(1)), using optimal space 𝒪(n log σ/log n). We then lift our ideas to the problem of computing a k-mismatch LCS, which has received ... : LIPIcs, Vol. 204, 29th Annual European Symposium on Algorithms (ESA 2021), pages 30:1-30:17 ...
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Keyword:
k mismatches; longest common substring; Theory of computation → Pattern matching; wavelet tree
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URL: https://dx.doi.org/10.4230/lipics.esa.2021.30 https://drops.dagstuhl.de/opus/volltexte/2021/14611/
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Bidirectional String Anchors: A New String Sampling Mechanism ...
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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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Longest Common Prefixes with $k$-Errors and Applications ...
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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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Linear-time computation of minimal absent words using suffix array
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Order-Preserving Suffix Trees and Their Algorithmic Applications ...
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