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A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

Authors Anadi Agrawal, Paweł Gawrychowski

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Anadi Agrawal
  • Institute of Computer Science, University of Wrocław, Poland
Paweł Gawrychowski
  • Institute of Computer Science, University of Wrocław, Poland

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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)
https://doi.org/10.4230/LIPIcs.ISAAC.2020.4

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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Longest Common Increasing Subsequence
  • Four Russians

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