Abstract
The approximate period recovery problem asks to compute all approximate word-periods of a given word S of length n: all primitive words P (\(|P|=p\)) which have a periodic extension at edit distance smaller than \(\tau _p\) from S, where \(\tau _p = \lfloor \frac{n}{(3.75+\epsilon )\cdot p} \rfloor \) for some \(\epsilon >0\). Here, the set of periodic extensions of P consists of all finite prefixes of \(P^\infty \).
We improve the time complexity of the fastest known algorithm for this problem of Amir et al. [Theor. Comput. Sci., 2018] from \({\mathcal {O}}(n^{4/3})\) to \({\mathcal {O}}(n \log n)\). Our tool is a fast algorithm for Approximate Pattern Matching in Periodic Text. We consider only verification for the period recovery problem when the candidate approximate word-period P is explicitly given up to cyclic rotation; the algorithm of Amir et al. reduces the general problem in \({\mathcal {O}}(n)\) time to a logarithmic number of such more specific instances.
J. Radoszewski and J. Straszyński—Supported by the “Algorithms for text processing with errors and uncertainties” project carried out within the HOMING programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund.
W. Rytter—Supported by the Polish National Science Center, grant no. 2014/13/B/ST6/00770.
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Kociumaka, T., Radoszewski, J., Rytter, W., Straszyński, J., Waleń, T., Zuba, W. (2018). Faster Recovery of Approximate Periods over Edit Distance. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_19
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