Summary
Efficient algorithms for computing the longest common subsequence (LCS for short) are discussed. O(pn) algorithm and O(p(m-p) log n) algorithm [Hirschberg 1977] seem to be best among previously known algorithms, where p is the length of an LCS and m and n are the lengths of given two strings (m≦n). There are many applications where the expected length of an LCS is close to m.
In this paper, O(n(m-p)) algorithm is presented. When p is close to m (in other words, two given strings are similar), the algorithm presented here runs much faster than previously known algorithms.
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References
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Nakatsu, N., Kambayashi, Y. & Yajima, S. A longest common subsequence algorithm suitable for similar text strings. Acta Informatica 18, 171–179 (1982). https://doi.org/10.1007/BF00264437
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DOI: https://doi.org/10.1007/BF00264437