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The Smith-Waterman algorithm is a dynamic programming technique used for local sequence alignment of biological sequences, such as DNA or proteins. It constructs a matrix where each cell represents the score of aligning substrings of the input sequences, using a scoring system that includes match, mismatch, and gap penalties. The algorithm fills the matrix based on the maximum score derived from neighboring cells, allowing for the identification of the best local alignment. The highest score in the matrix indicates the optimal local alignment, and backtracking is used to retrieve the aligned sequences.

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