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

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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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