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.2020.15
URN: urn:nbn:de:0030-drops-121406
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12140/
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Golan, Shay ; Kociumaka, Tomasz ; Kopelowitz, Tsvi ; Porat, Ely

The Streaming k-Mismatch Problem: Tradeoffs Between Space and Total Time

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Abstract

We revisit the k-mismatch problem in the streaming model on a pattern of length m and a streaming text of length n, both over a size-σ alphabet. The current state-of-the-art algorithm for the streaming k-mismatch problem, by Clifford et al. [SODA 2019], uses Õ(k) space and Õ(√k) worst-case time per character. The space complexity is known to be (unconditionally) optimal, and the worst-case time per character matches a conditional lower bound. However, there is a gap between the total time cost of the algorithm, which is Õ(n√k), and the fastest known offline algorithm, which costs Õ(n + min(nk/√m, σn)) time. Moreover, it is not known whether improvements over the Õ(n√k) total time are possible when using more than O(k) space.
We address these gaps by designing a randomized streaming algorithm for the k-mismatch problem that, given an integer parameter k≤s≤m, uses Õ(s) space and costs Õ(n+min(nk²/m, nk/√s, σnm/s)) total time. For s=m, the total runtime becomes Õ(n + min(nk/√m, σn)), which matches the time cost of the fastest offline algorithm. Moreover, the worst-case time cost per character is still Õ(√k).

BibTeX - Entry

@InProceedings{golan_et_al:LIPIcs:2020:12140,
  author =	{Shay Golan and Tomasz Kociumaka and Tsvi Kopelowitz and Ely Porat},
  title =	{{The Streaming k-Mismatch Problem: Tradeoffs Between Space and Total Time}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12140},
  URN =		{urn:nbn:de:0030-drops-121406},
  doi =		{10.4230/LIPIcs.CPM.2020.15},
  annote =	{Keywords: Streaming pattern matching, Hamming distance, k-mismatch}
}

Keywords: Streaming pattern matching, Hamming distance, k-mismatch
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020

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