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 has children. Each child of the root contains 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]
References
[edit]- ^ Berkman, Omer; Schieber, Baruch; Vishkin, Uzi (1993), "Optimal doubly logarithmic parallel algorithms based on finding all nearest smaller values", Journal of Algorithms, 14 (3): 344–370, CiteSeerX 10.1.1.55.5669, doi:10.1006/jagm.1993.1018
- ^ Harald Prokop. Cache-Oblivious Algorithms. Masters thesis, MIT. 1999.
Further reading
[edit]- 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.