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arXiv · 2003.13589

A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem

Anadi Agrawal·Paweł Gawrychowski
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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 applicable to LCIS. Recently, Duraj [STACS 2020] used a completely different method based on the combinatorial properties of LCIS to design an $\mathcal{O}(n^2(\log\log n)^2/\log^{1/6}n)$ time algorithm. We show that an approach based on exploiting tabulation can be used to construct an asymptotically faster $\mathcal{O}(n^2 \log\log n/\sqrt{\log n})$ 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, Paweł Gawrychowski. 2020-03-30. A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem. https://arxiv.org/abs/2003.13589

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