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DOI: 10.4230/LIPIcs.ISAAC.2020.4

A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

Authors: Anadi Agrawal and Paweł Gawrychowski

Published in: LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Abstract

The Longest Common Increasing Subsequence (LCIS) is a variant of the classical Longest Common Subsequence (LCS), in which we additionally require the common subsequence to be strictly increasing. While the well-known "Four Russians" technique can be used to find LCS in subquadratic time, it does not seem directly applicable to LCIS. Recently, Duraj [STACS 2020] used a completely different method based on the combinatorial properties of LCIS to design an 𝒪(n²(log log n)²/log^{1/6}n) time algorithm. We show that an approach based on exploiting tabulation (more involved than "Four Russians") can be used to construct an asymptotically faster 𝒪(n² log log n/√{log n}) time algorithm. As our solution avoids using the specific combinatorial properties of LCIS, it can be also adapted for the Longest Common Weakly Increasing Subsequence (LCWIS).

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Anadi Agrawal and Paweł Gawrychowski. A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 4:1-4:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{agrawal_et_al:LIPIcs.ISAAC.2020.4,
  author =	{Agrawal, Anadi and Gawrychowski, Pawe{\l}},
  title =	{{A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{4:1--4:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Cao, Yixin and Cheng, Siu-Wing and Li, Minming},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.4},
  URN =		{urn:nbn:de:0030-drops-133487},
  doi =		{10.4230/LIPIcs.ISAAC.2020.4},
  annote =	{Keywords: Longest Common Increasing Subsequence, Four Russians}
}

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A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

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