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.FSTTCS.2018.40
URN: urn:nbn:de:0030-drops-99390
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9939/
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Bringmann, Karl ; Chaudhury, Bhaskar Ray

Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS

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Abstract

We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size |Sigma|. For the problem of deciding whether the LCS of strings x,y has length at least L, we obtain a sketch size and streaming space usage of O(L^{|Sigma| - 1} log L). We also prove matching unconditional lower bounds.
As an application, we study a variant of LCS where each alphabet symbol is equipped with a weight that is given as input, and the task is to compute a common subsequence of maximum total weight. Using our sketching algorithm, we obtain an O(min{nm, n + m^{|Sigma|}})-time algorithm for this problem, on strings x,y of length n,m, with n >= m. We prove optimality of this running time up to lower order factors, assuming the Strong Exponential Time Hypothesis.

BibTeX - Entry

@InProceedings{bringmann_et_al:LIPIcs:2018:9939,
  author =	{Karl Bringmann and Bhaskar Ray Chaudhury},
  title =	{{Sketching, Streaming, and Fine-Grained Complexity of (Weighted) LCS}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{40:1--40:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9939},
  URN =		{urn:nbn:de:0030-drops-99390},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.40},
  annote =	{Keywords: algorithms, SETH, communication complexity, run-length encoding}
}

Keywords: algorithms, SETH, communication complexity, run-length encoding
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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