License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2019.31
URN: urn:nbn:de:0030-drops-105029
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10502/
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Merkurev, Oleg ; Shur, Arseny M.

Searching Long Repeats in Streams

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LIPIcs-CPM-2019-31.pdf (1 MB)

Abstract

We consider two well-known related problems: Longest Repeated Substring (LRS) and Longest Repeated Reversed Substring (LRRS). Their streaming versions cannot be solved exactly; we show that only approximate solutions by Monte Carlo algorithms are possible, and prove a lower bound on consumed memory. For both problems, we present purely linear-time Monte Carlo algorithms working in O(E + n/E) space, where E is the additive approximation error. Within the same space bounds, we then present nearly real-time solutions, which require O(log n) time per symbol and O(n + n/E log n) time overall. The working space exactly matches the lower bound whenever E=O(n^{0.5}) and the size of the alphabet is Omega(n^{0.01}).

BibTeX - Entry

@InProceedings{merkurev_et_al:LIPIcs:2019:10502,
  author =	{Oleg Merkurev and Arseny M. Shur},
  title =	{{Searching Long Repeats in Streams}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Nadia Pisanti and Solon P. Pissis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10502},
  URN =		{urn:nbn:de:0030-drops-105029},
  doi =		{10.4230/LIPIcs.CPM.2019.31},
  annote =	{Keywords: Longest repeated substring, longest repeated reversed substring, streaming algorithm, Karp, Rabin fingerprint, suffix tree}
}

Keywords: Longest repeated substring, longest repeated reversed substring, streaming algorithm, Karp, Rabin fingerprint, suffix tree
Collection: 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)
Issue Date: 2019
Date of publication: 06.06.2019

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