[freefrag]

What's the advantage of using wider trees at every level? Asymptotically wouldn't you get the same behaviour with a binary tree?

[hit9]

Advantage: constant level time complexity with better space utilization.

The binary tree with the binary-search searching strategy has a time complexity O(logN), which is higher than htree's.

This htree is mainly for memory bounded cases.

[aweinstock]

Higher branching factor gets you a better constant factor because the depth of the tree is the base-(branching factor) logarithm of the number of nodes. The number of pointers you need to follow to reach a leaf is equal to the depth of the tree, and pointer-dereferences are likely to cause a cache miss, which is a relatively slow operation.

You're correct that asymptotically, it's the same thing.