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arXiv · 2006.00216

Longest Square Subsequence Problem Revisited

Takafumi Inoue·Shunsuke Inenaga·Hideo Bannai
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Abstract

The longest square subsequence (LSS) problem consists of computing a longest subsequence of a given string $S$ that is a square, i.e., a longest subsequence of form $XX$ appearing in $S$. It is known that an LSS of a string $S$ of length $n$ can be computed using $O(n^2)$ time [Kosowski 2004], or with (model-dependent) polylogarithmic speed-ups using $O(n^2 (\log \log n)^2 / \log^2 n)$ time [Tiskin 2013]. We present the first algorithm for LSS whose running time depends on other parameters, i.e., we show that an LSS of $S$ can be computed in $O(r \min\{n, M\}\log \frac{n}{r} + n + M \log n)$ time with $O(M)$ space, where $r$ is the length of an LSS of $S$ and $M$ is the number of matching points on $S$.

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Takafumi Inoue, Shunsuke Inenaga, Hideo Bannai. 2020-05-30. Longest Square Subsequence Problem Revisited. https://arxiv.org/abs/2006.00216

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