Doubly logarithmic tree

In computer science, a doubly logarithmic tree is a tree where each internal node of height 1, the tree layer above the leaves, has two children, and each internal node of height $h>1$ has $2^{2^{h-2}}$ children. Each child of the root contains $\sqrt{n}$ leaves. The number of children at a node from each leaf to root is 0,2,2,4,16, 256, 65536, ... (sequence A001146 in the OEIS)

One dot at the top has two lines connecting to other dots.

A double log tree

A similar tree called a k-merger is used in Prokop et al.'s cache oblivious Funnelsort to merge elements.

Further reading

• M. Frigo, C.E. Leiserson, H. Prokop, and S. Ramachandran. Cache-oblivious algorithms. In Proceedings of the 40th IEEE Symposium on Foundations of Computer Science (FOCS 99), p. 285-297. 1999. Extended abstract at IEEE, at Citeseer.
• Demaine, Erik. Review of the Cache-Oblivious Sorting. Notes for MIT Computer Science 6.897: Advanced Data Structures.