A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem
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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 O(n^2(loglog n)^2/log^1/6n) time algorithm. We show that an approach based on exploiting tabulation can be used to construct an asymptotically faster O(n^2 loglog 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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