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Since you appear to have nucleic acid strings, perhaps you could leverage the minimal alphabet used to pre-compute differences. Assuming each position can only be represented by 5 characters (A, C, T, G and -) then taking 4 characters at a time, there can only be 625 possible strings. Comparing two such sub strings means there are only 390,625 possible pairs - surely small enough to fit into memory.
I do realize that you have to keep track of which "quad" you are comparing so that your position comes out right but this is hardly significant. Even comparing 5 characters at a time is less than 10 million parings so depending on your memory constraints you may not be limited to quads. Of course, if your strings can have more than 5 characters at each position you will have to do fewer at a time.
If you need an implementation of this, let me know but I think it should be fairly obvious.
Cheers - L~R