Exponential tree

Exponential tree
Type	tree
Invented	1995
Invented by	Arne Andersson
Time complexity in big O notation Operation Average Worst case Search O(min(√log n, log n/log w+ log log n, log w log log n)) O(min(√log n, log n/log w+ log log n, log w log log n)) Insert O(min(√log n, log n/log w+ log log n, log w log log n)) O(min(√log n, log n/log w+ log log n, log w log log n)) Delete O(min(√log n, log n/log w+ log log n, log w log log n)) O(min(√log n, log n/log w+ log log n, log w log log n)) Space complexity Space O(n) O(n)

An exponential tree is almost identical to a binary search tree, with the exception that the dimension of the tree is not the same at all levels. In a normal binary search tree, each node has a dimension (d) of 1, and has 2^d children. In an exponential tree, the dimension equals the depth of the node, with the root node having a d = 1. So the second level can hold four nodes, the third can hold eight nodes, the fourth 16 nodes, and so on.

External links

• Faster deterministic sorting and searching in linear space (Original paper from '95)
• Laying out and Visualizing Large Trees Using a Hyperbolic Space
• Implementation and Performance Analysis of Exponential Tree Sorting (This paper is not correct)