We are talking about a brute force, exhaustive search method versus algorithms which have significantly better time complexities. I don't understand how the word "approximate" applies to these algorithms which are largely or entirely deterministic, but sequence alignment is an inherently approximate question. You want your answer to be approximate, because mismatches and gaps are real things. In fact, finding the "approximate" answers are what the OP is after - places in the genome that look like, but aren't exactly, the query sequence. And as soon as you expand your query length or edit distance even a little, finding that becomes completely infeasible. In fact, the OP lucked out because this is a very special circumstance (this method is completely computationally infeasible for 99/100 applications of this problem).