In semi-global AKA glocal alignment (definitions can be found here and here), the most common implementation is to adapt Needleman-Wunsch's algorithm. One of the modifications is to start the traceback at the greatest element of the last row of the alignment matrix AKA scores matrix (or last column, if there are more rows than columns) instead of starting the traceback at the absolute last element of the matrix. Here is a visual comparison:
But what if there are two equally greatest elements in the last row?
I've encountered such situation when re-implementing the algorithm - my first implementation, when looking for the greatest element, started looking from the beginning of the row, my newer implementation starts from the end. In one particular case the row was like below
0 // I = 0 . . . 4962 // I = 2481 4962 // I = 2482
So my first implementation would start the traceback at 2481, whereas my last implementation starts at 2482, giving two different alignments with two different scores. Which one is correct?
Intuitively I'd say using the smaller index is correct, since the whole point of doing a semi-global alignment is to have non penalized end gaps. And indeed in such case it gave the greatest score, but I'm not sure if that would be the case with a different sequence. I couldn't find anything on the subject. Thanks.