How to select a subsample of fixed size to maximize its total PCA variance? I would like to use PCA to help design my genomics experiment. 
I can only afford to perform my experiment on a limited number of genotypes so would like to maximize the variation of the ones I select. I have several 100k SNPs for each of ~300 genotypes. If I perform PCA on them, how can I select a subsample that maximizes the variation for a sample that size?
Ideally I could then weigh up the benefits of increasing the number of genotypes vs. proportion of the total variation captured in the subsample.  
Also, say I already have some of the genotype samples; could I ask what proportion of the total variation they already encompass?   
 A: PCA might be a good way to go, as the first principal component direction finds the direction with largest eigenvalue (and thereby most variation). This direction vector is also called weight or loading vector.
It does not however, guarantee that the solution is sparse, in that case you can approach more heuristically as amoeba suggested and exclude genotypes that have little influence on the direction. This is assuming that the software (and function) you are using can give your the direction and not just the component. If you perchance is using R and the function princomp(), you are looking for the first column of the loadings-matrix.
Hope that helped.
Note: The loadings-matrix found using the princomp()-function leaves values below a certain threshold blank, but they are not necessarily zero. It could however be a good place to start your heuristic search.
Update: I misunderstood the question, my bad. However, to actually answer your question it is a general concept mostly used within medical research, and is called maximum variation sampling. As far as I know, there is no neat way of achieving the maximum variation, as in medical research it is mostly used when dealing with small samples, as amoeba also suggested. With that being said, you might be able to find an algorithm somewhere on the internet, or you need to attack the problem heuristically.
