Smith – Waterman Algorithm 

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. Backtracking starts at the highest scoring matrix cell and proceeds until a cell with score zero is encountered, yielding the highest scoring local alignment. One does not actually implement the algorithm as described because improved alternatives are now available that have better scaling (Gotoh, 1982) and are more accurate (Altschul and Erickson, 1986). (Wikipedia)