Interleave in peace, or interleave in pieces

Bit interleaving is a technique that sometimes can collapse a problem of high dimensional data to one of lower dimensional data. Our favorite use is going from two or three dimensions to one dimension. Of course, you lose something in this process because 2D is not the same as 1D. There is no "reasonable" one-to-one mapping between the two spaces. But sometimes, what you lose isn't all that important, and what you gain might make it worth doing. We show how we have used bit interleaving for two applications: finding the Hausdorff distance between sets (approximately) and calculating capacity dimension.