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 ${\displaystyle h>1}${\displaystyle h>1} has ${\displaystyle 2^{2^{h-2}}}${\displaystyle 2^{2^{h-2}}} children. Each child of the root contains ${\displaystyle {\sqrt {n}}}${\displaystyle {\sqrt {n}}} leaves.^[1] 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)

A similar tree called a k-merger is used in Prokop et al.'s cache oblivious Funnelsort to merge elements.^[2]

• 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.

• Trees (data structures)

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