New Algorithms for the LCS Problem

The LCS problem is to determine a longest common subsequence (LCS) of two symbol sequences. Two algorithms which improve two existing results, respectively, are presented. Let m, n be the lengths of the two input strings, with m Q n, p being the length of the LCS, and s being the number of distinct symbols appearing in the two strings. It is shown that the first algorithm presented requires at most O(n log s) preprocessing time and O@m log(n/m) + pm) processing time to solve the problem. This bound is better than that of previous algorithms especially when n is much greater than m. The algorithm also exhibits desirable properties under conditions of sparse matches. The second scheme achieves essentially the same bound (O@m log(n/p) + pm)) by employing efficient merging methods in the computations. It also outperforms existing algorithms designed for sparsely-matched situations. Together, the two algorithms provide interesting contrasts of different approaches to one problem; they also

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