In this work, we show two streaming algorithms for computing the length of the shortest cover of a string of length n. We start by showing a two-pass algorithm that uses O(log^2 n) space and then show a one-pass streaming algorithm that uses O(sqrt{n log n}) space. Both algorithms run in near-linear time. The algorithms are randomized and compute the answer incorrectly with probability inverse-polynomial in n. We also show that there is no sublinear-space streaming algorithm for computing the length of the shortest seed of a string.
@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2019.22, author = {Gawrychowski, Pawe{\l} and Radoszewski, Jakub and Starikovskaya, Tatiana}, title = {{Quasi-Periodicity in Streams}}, booktitle = {30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)}, pages = {22:1--22:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-103-0}, ISSN = {1868-8969}, year = {2019}, volume = {128}, editor = {Pisanti, Nadia and P. Pissis, Solon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.22}, URN = {urn:nbn:de:0030-drops-104930}, doi = {10.4230/LIPIcs.CPM.2019.22}, annote = {Keywords: Streaming algorithms, quasi-periodicity, covers, seeds} }
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