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arXiv · 2002.06796

Detecting $k$-(Sub-)Cadences and Equidistant Subsequence Occurrences

Mitsuru Funakoshi·Yuto Nakashima·Shunsuke Inenaga·Hideo Bannai·Masayuki Takeda·Ayumi Shinohara
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Abstract

The equidistant subsequence pattern matching problem is considered. Given a pattern string $P$ and a text string $T$, we say that $P$ is an \emph{equidistant subsequence} of $T$ if $P$ is a subsequence of the text such that consecutive symbols of $P$ in the occurrence are equally spaced. We can consider the problem of equidistant subsequences as generalizations of (sub-)cadences. We give bit-parallel algorithms that yield $o(n^2)$ time algorithms for finding $k$-(sub-)cadences and equidistant subsequences. Furthermore, $O(n\log^2 n)$ and $O(n\log n)$ time algorithms, respectively for equidistant and Abelian equidistant matching for the case $|P| = 3$, are shown. The algorithms make use of a technique that was recently introduced which can efficiently compute convolutions with linear constraints.

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Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, Ayumi Shinohara. 2020-02-17. Detecting $k$-(Sub-)Cadences and Equidistant Subsequence Occurrences. https://arxiv.org/abs/2002.06796

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