Abstract
Although a number of efficient algorithms for the longest common subsequence (LCS) problem have been suggested since the 1970's, there is no duality theorem for the LCS problem. In the present paper a simple duality theorem is proved for the LCS problem and for a wide class of partial orders generalizing the notion of common subsequence. An algorithm for finding generalized LCS is suggested which has the classical dynamic programming algorithm as a special case. It is shown that the generalized LCS problem is closely associated with the minimal Hilbert basis problem. The Jeroslav-Schrijver characterization of minimal Hilbert bases gives an O(n) estimation for the number of elementary edit operations for generalized LCS.
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© 1992 Springer-Verlag Berlin Heidelberg
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Pevzner, P.A., Waterman, M.S. (1992). Matrix longest common subsequence problem, duality and hilbert bases. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1992. Lecture Notes in Computer Science, vol 644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56024-6_7
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DOI: https://doi.org/10.1007/3-540-56024-6_7
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