Have you got any links on how to do that, as it sounds very like a problem I am trying to sole just now - combinations of DNA sequences that work together on a sequencing machine.

At the moment I am self joining a table of the sequences to itself in MySQL, but after a certain number of self joins the table gets massive. Time to compute is more the problem rather than storage space though, as I am only storing the ones that work (> 2 mismatches in the sequence). Would Map Reduce help in this scenario?

If I had your problem, the first thing that I would do is try PostgreSQL to see if it does the joins fast enough. Second thing that I would try is to put the data in a SOLR db and translate the queries to a SOLR base query (q=) plus filter queries (fq=) on top.

Only if both of these fail to provide sufficient performance, would I look at a map reduce solution based on the Hadoop ecosystem. Actually, I wouldn't necessarily use the Hadoop ecosystem. It has a lot of parts/layers and the newer and generally better parts are not as well known so it is a bit more leading edge than lots of folks like. I'd also look at somethink like Riak http://docs.basho.com/riak/latest/dev/using/mapreduce/ because then you have your data storage and clustering issues solved in a bulletproof way (unlike Mongo) but you can do MapReduce as well.