Consider two strings A and B of lengths n and m respectively, with n m. The problem of computing global and local alignments between a and all m~2 substrings of B can be solved by the classical Needleman-Wunsch and Smith-Waterman algorithms, respectively, which takes O(m~2n) time and O(m~2) space. This paper proposes faster algorithms that take O(mn~2) time and O(mn) space. The improvement stems from a compact way to represent all the alignment scores.
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