Doubly logarithmic tree explained

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, ... A similar tree called a k-merger is used in Prokop et al.'s cache oblivious Funnelsort to merge elements.^[1]

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.

Notes and References

1. Harald Prokop. Cache-Oblivious Algorithms. Masters thesis, MIT. 1999.