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Quasi-Periodicity in Streams

Authors Paweł Gawrychowski, Jakub Radoszewski, Tatiana Starikovskaya

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Author Details

Paweł Gawrychowski
  • University of Wrocław, 50-137 Wrocław, Poland
Jakub Radoszewski
  • Institute of Informatics, University of Warsaw, 02-097 Warsaw, Poland
Tatiana Starikovskaya
  • DIENS, École normale supérieure, PSL Research University, 75005 Paris, France

Funding

Jakub Radoszewski is 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.

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Paweł Gawrychowski, Jakub Radoszewski, and Tatiana Starikovskaya. Quasi-Periodicity in Streams. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CPM.2019.22

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • Streaming algorithms
  • quasi-periodicity
  • covers
  • seeds

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