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 e?'a(n?2(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 e?'a(n?2 log log n/a^S{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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机译：最长的常见增加随后（LCIS）是古典最长常见的子序列（LCS）的变体，其中我们另外需要严格增加常见的子序列。虽然众所周知的“四个俄罗斯人”技术可用于在子例时找到LCS，但它看起来不会直接适用于LCIS。最近，Duraj [Stacs 2020]使用了基于LCI的组合特性的完全不同的方法来设计E？'A（n？2（日志log n）？2 / log ^ {1/6} n）时间算法。我们展示了一种基于利用表格的方法（比“四个俄语”）可以使用较快的渐近渐近的渐近e？'（n？2 log log n / a ^ s {log n}）时间算法。由于我们的解决方案避免使用LCIS的特定组合性质，因此也可以适用于最长的常见弱越来越多的子序列（LCWI）。
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