Exponential tree

An exponential tree is a type of search tree where the number of children of its nodes decreases doubly-exponentially with increasing depth. Values are stored only in the leaf nodes. Each node contains a splitter, a value less than or equal to all values in the subtree which is used during search. Exponential trees use another data structure in inner nodes containing the splitters from children, allowing fast lookup.

Exponential tree
Typetree
Invented1995
Invented byArne 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)

Exponential trees achieve optimal asymptotic complexity on some operations. They have mainly theoretical importance.

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