Abstract
The known 2-string LCS problem is generalized to finding a Longest Common Subsequence (LCS) for a set of strings. A new, general approach that systematically enumerates common subsequences is proposed for the solution. Assuming a finite symbol set, it is shown that the presented scheme requires a preprocessing time that grows linearly with the total length of the input strings and a processing time that grows linearly with (K), the number of strings, and (∥ℙ∥) the number of matches among them. The only previous algorithm for the generalized LCS problem takesO(K·|S 1|·|S 2|·...|S k |) execution time, where |S i | denotes the length of the stringS i . Since typically ∥ℙ∥ is a very small percentage of |S 1|·|S 2|·...·|S k |, the proposed method may be considered to be much more efficient than the straightforward dynamic programming approach.
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Hsu, W.J., Du, M.W. Computing a longest common subsequence for a set of strings. BIT 24, 45–59 (1984). https://doi.org/10.1007/BF01934514
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DOI: https://doi.org/10.1007/BF01934514