Smith-Waterman algorithm

The Smith–Waterman algorithm performs local sequence alignment; that is, for determining similar regions between two strings of nucleic acid sequences or protein sequences. Instead of looking at the entire sequence, the Smith–Waterman algorithm compares segments of all possible lengths and optimizes the similarity measure.

The algorithm was first proposed by Temple F. Smith and Michael S. Waterman in 1981. Like the Needleman–Wunsch algorithm, of which it is a variation, Smith–Waterman is a dynamic programming algorithm. As such, it has the desirable property that it is guaranteed to find the optimal local alignment with respect to the scoring system being used (which includes the substitution matrix and the gap-scoring scheme). The main difference to the Needleman–Wunsch algorithm is that negative scoring matrix cells are set to zero, which renders the (thus positively scoring) local alignments visible. Traceback procedure starts at the highest scoring matrix cell and proceeds until a cell with score zero is encountered, yielding the highest scoring local alignment. Because of its cubic computational complexity in time and quadratic complexity in space, it often cannot be practically applied to large-scale problems and is replaced in favor of less general but computationally more efficient alternatives such as (Gotoh, 1982), (Altschul and Erickson, 1986), and (Myers and Miller 1988).

In 1970, Saul B. Needleman and Christian D. Wunsch proposed a heuristic homology algorithm for sequence alignment, also referred to as the Needleman–Wunsch algorithm. It is a global alignment algorithm that requires ${\displaystyle O(mn)}$ calculation steps (${\displaystyle m}$ and ${\displaystyle n}$ are the lengths of the two sequences being aligned). It uses the iterative calculation of a matrix for the purpose of showing global alignment. In the following decade, Sankoff, Reichert, Beyer and others formulated alternative heuristic algorithms for analyzing gene sequences. Sellers introduced a system for measuring sequence distances. In 1976, Waterman et al. added the concept of gaps into the original measurement system. In 1981, Smith and Waterman published their Smith–Waterman algorithm for calculating local alignment.

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