Papers › Efficient algorithms for the longest common subsequence in k-length substrings
Efficient algorithms for the longest common subsequence in k-length substrings
Sebastian Deorowicz, Szymon Grabowski
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Finding the longest common subsequence in k-length substrings (LCS$k$) is a recently proposed problem motivated by computational biology. This is a generalization of the well-known LCS problem in which matching symbols from two sequences A and B are replaced with matching non-overlapping substrings of length k from A and B. We propose several algorithms for LCS$k$, being non-trivial incarnations of the major concepts known from LCS research (dynamic programming, sparse dynamic programming, tabulation). Our algorithms make use of a linear-time and linear-space preprocessing finding the occurrences of all the substrings of length k from one sequence in the other sequence.
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