We are here intererested in finding an optimal alignment between
a part of *x* and a part of *y*.

The notion of distance is not suitable anymore to get the result thus we have to use the notion of similarity.

We use the following recurrence formula ([18]):

where substitutions, deletions and insertions are given negative values.

To find an optimal local alignment, it is sufficient to find
the largest value in the table *T* and to trace back the path
from the square containing this value.

Example :

*x* = `YHCQPGK`,
*y* = `LAHYQQKPGKA`,
*Sub*(*a*,*a*) = 1,
*Sub*(*a*,*b*) = -3,
*Del*(*a*) = *Ins*(*a*) = -1.

`PGK` corresponds to the highest area of similarity between
`YWCQPGK` and `LAWYQQKPGKA`.

e-mails: {Christian.Charras, Thierry.Lecroq}@laposte.net