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The constrained LCS problem asks one to find a longest common subsequence oftwo input strings $A$ and $B$ with some constraints. The STR-IC-LCS problem isa variant of the constrained LCS problem, where the solution must include agiven constraint string $C$ as a substring. Given two strings $A$ and $B$ ofrespective 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, proposedby 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-LCSproblem, 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, ouralgorithm is always as fast as Deorowicz's algorithm, and is faster when inputstrings are compressible via RLE.

Faster STR-IC-LCS computation via RLE