[mmalone]

If you're tempted to use space filling curves (z-curves, hilbert curves, etc.) you should take a look at simple multi-dimensional data structures as an alternative.

As a couple of people have mentioned in this thread, space filling curves aren't great at preserving locality (i.e., two points that are "close together" in two dimensional space might end up being "far apart" in one dimensional space, and vice versa). A k-d tree is easy to code up and, in general, will be more efficient for queries like k-NN than dimensionality reduction because it's better at preserving locality.

There are also good libraries for multi-dimensional data structures for pretty much any mainstream language.