Variations on dynamic programming
d(i,j)= min
{
d(i-1,j)+ g
d(i,j-1)+ g
d(i-1,j-1) + t(vi,wj)
t(vi,wj) = m if vi=wj
t(vi,wj) = n if vi ? wj
g - gap penalty (e.g. 2)
m - match score (e.g. -1)
n - mismatch score (e.g.+1)
(In practice signs are reversed and the max is taken, and the highest overall score is the most significant )
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