Algorithms for the Merged-LCS Problem and Its Variant with Block Constraint
نویسندگان
چکیده
The longest common subsequence (LCS) problem was widely discussed and regarded as the measurement for the relationship among sequences. Let A′ and B′ are the subsequences of A and B, respectively. The merged-sequence E(A,B) is composed of A′ and B′. In this paper, we consider the merged-LCS problem, denoted as LCS(T, E(A,B)), for measuring the relationship among three sequences T , A and B. We first propose an algorithm for solving the merged-LCS problem, whose time complexity is O(n), where n is the sequence length. We further discuss the variant version of the merged-LCS problem with block constraint, that is, the block information of A and B is given in advance. For the blocked mergedLCS problem, we propose an algorithm with time complexity O(nm), where m is the number of blocks. An improved O(n + nm) algorithm is proposed for the same blocked merged-LCS problem by using the concept of preprocessing.
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