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.STACS.2020.41
URN: urn:nbn:de:0030-drops-119020
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11902/
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Duraj, Lech

A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem

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LIPIcs-STACS-2020-41.pdf (0.6 MB)

Abstract

The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated Longest Common Subsequence (LCS) problem. For LCIS, as well as for LCS, there is an ?(n²)-time algorithm and a SETH-based conditional lower bound of ?(n^{2-ε}). For LCS, there is also the Masek-Paterson ?(n²/log n)-time algorithm, which does not seem to adapt to LCIS in any obvious way. Hence, a natural question arises: does any (slightly) sub-quadratic algorithm exist for the Longest Common Increasing Subsequence problem? We answer this question positively, presenting a ?(n²/log^a n)-time algorithm for a = 1/6-o(1). The algorithm is not based on memorizing small chunks of data (often used for logarithmic speedups, including the "Four Russians Trick" in LCS), but rather utilizes a new technique, bounding the number of significant symbol matches between the two sequences.

BibTeX - Entry

@InProceedings{duraj:LIPIcs:2020:11902,
  author =	{Lech Duraj},
  title =	{{A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{41:1--41:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11902},
  URN =		{urn:nbn:de:0030-drops-119020},
  doi =		{10.4230/LIPIcs.STACS.2020.41},
  annote =	{Keywords: longest common increasing subsequence, log-shaving, matching pairs}
}

Keywords: longest common increasing subsequence, log-shaving, matching pairs
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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