What prevents Van Emde Boas trees from being more popular in real-world applications?

Question

We know balanced trees perform insertion, deletion, and search in O(log n)-time, examples include

• Red-Black
• AVL
• Splay
• B-tree (a

Answer 1

The asymptotic complexity is sometimes misleading. In the case for Van Emde Boas tree the constant is quite large see here. I quote:

However, for small trees the overhead associated with vEB trees
is enormous: on the order of 2^(m/2)

There are also other cases where an algorithm with better complexity exists but it only gets better for an input so big that in practice it is almost never used e.g. linear time static RMQ.