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arXiv · 1703.04954

Faster STR-IC-LCS computation via RLE

Keita Kuboi·Yuta Fujishige·Shunsuke Inenaga·Hideo Bannai·Masayuki Takeda
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Abstract

The constrained LCS problem asks one to find a longest common subsequence of two input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem is a variant of the constrained LCS problem, where the solution must include a given constraint string $C$ as a substring. Given two strings $A$ and $B$ of respective lengths $M$ and $N$, and a constraint string $C$ of length at most $\min\{M, N\}$, the best known algorithm for the STR-IC-LCS problem, proposed by Deorowicz~({\em Inf. Process. Lett.}, 11:423--426, 2012), runs in $O(MN)$ time. In this work, we present an $O(mN + nM)$-time solution to the STR-IC-LCS problem, where $m$ and $n$ denote the sizes of the run-length encodings of $A$ and $B$, respectively. Since $m \leq M$ and $n \leq N$ always hold, our algorithm is always as fast as Deorowicz's algorithm, and is faster when input strings are compressible via RLE.

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Keita Kuboi, Yuta Fujishige, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda. 2017-03-15. Faster STR-IC-LCS computation via RLE. https://arxiv.org/abs/1703.04954

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