Needleman–Wunsch and Smith Waterman Algorithm

The Needleman–Wunsch algorithm (1970) is a dynamic programming method used for global sequence alignment, i.e., it aligns two sequences from beginning to end by introducing gaps where necessary. It ensures the best possible alignment across the entire length of both sequences.

The Smith–Waterman algorithm (1981) is a dynamic programming method used for local sequence alignment, i.e., it finds the most similar subsequence between two sequences. Unlike the Needleman–Wunsch algorithm, which aligns the full length of both sequences (global alignment), Smith–Waterman identifies high-scoring regions even if the sequences as a whole are not very similar.