Local Alignment

In many applications two strings may not be highly similar as a whole, but many contain regions that are highly similar. The task is to find and extract a pair of regions, one from each of the two given strings, that exhibit high similarity. This is called the local alignment or local similarity problem and is defined formally below:

 

Example 2.13   Consider the two strings:
S = a b c x d e x
T = x x x c d e
If we give each match a value of 2 and each mismatch a value of -1, then the two substrings: ${\alpha}$ = cxde and ${\beta}$ = c-de of S and T respectively have the optimal alignment.