Lecture 4 Optimal Local Alignment , and Gaps January 11 , 1996 Lecturer : Martin Tompa

The dynamic programming algorithm for optimal local alignment is similar to the dynamic programming algorithm for optimal global alignment given in Section 3.3. It proceeds by filling in a table with the values of v(i; j), with i; j increasing. The value of each entry is calculated according to a new basis and recurrence for v(i; j), given below. Unlike the global alignment algorithm, however, the value of the optimal local alignment can be any entry, whichever contains the maximum of all (n+ 1)(m + 1) values of v(i; j). The reason for this is that each v(i; j) entry represents an optimal pair ( ; ) of suffixes of a given pair (i; j) of prefixes. Since a suffix of a prefix is just a substring, we find the optimal pair of substrings by maximizing v(i; j) over all possible prefix pairs (i; j).