Understanding Fusion Trees?

Question

I stumbled across the Wikipedia page for them:

Fusion tree

And I read the class notes pdfs linked at the bottom, but it gets hand-wavy about the data structure i

Answer 1

The idea behind the fusion tree is actually fairly simple. Suppose you have w-bit (say 64 bit) keys, the idea is to compress (i.e. sketching) every consecutive 64 keys in to an 64-element array. The sketching function assures a constant time mapping between the original keys and the array index for a given group. Then searching for the key becomes searching for the group containing the key, which is O(log(n/64)). As you can see, the main challenge is the sketching function.