New Tabulation and Sparse Dynamic Programming Based Techniques for Sequence Similarity Problems
نویسنده
چکیده
Calculating the length of a longest common subsequence (LCS) of two strings A and B of length n andm is a classic research topic, with many worst-case oriented results known. We present two algorithms for LCS length calculation with respectively O(mn log log n/ log n) and O(mn/ log n+r) time complexity, the latter working for r = o(mn/(log n log log n)), where r is the number of matches in the dynamic programming matrix. We also describe conditions for a given problem sufficient to apply our techniques, with several concrete examples presented, namely the edit distance, LCTS and MerLCS problems.
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تاریخ انتشار 2014