Find a way to detect whether two dna strings are similar

One way of doing this is to find the longest common subsequence, since we can allow to have to strings that are also having different genes interleaved. So suppose you have {ACGGAGGGAA} and {ACGAAGG} what is the longest common subsequence? {ACGAGG}

Solution: either direct DP or reducing this to Longest non decreasing subsequence problem.