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van Emde Boas tree
Type
Non-binary tree
Invented
1975
Invented by
Peter van Emde Boas
Time complexity in big O notation
Operation
Average
Worst case
Search
Insert
Delete
Space complexity
Space
A van Emde Boas tree (Dutch pronunciation:[vɑnˈɛmdəˈboːɑs]), also known as a vEB tree or van Emde Boas priority queue, is a tree data structure which implements an associative array with m-bit integer keys. It was invented by a team led by Dutch computer scientist Peter van Emde Boas in 1975.[1] It performs all operations in O(log m) time (assuming that an bit operation can be performed in constant time), or equivalently in time, where is the largest element that can be stored in the tree. The parameter is not to be confused with the actual number of elements stored in the tree, by which the performance of other tree data-structures is often measured.
The standard vEB tree has inadequate space efficiency. For example, for storing 32-bit integers (i.e., when , it requires bits of storage. However, similar data structures with equally good time efficiency and with space efficiency of exist, where is the number of stored elements, and vEB trees can be modified to require only space.
^Peter van Emde Boas: Preserving order in a forest in less than logarithmic time (Proceedings of the 16th Annual Symposium on Foundations of Computer Science 10: 75-84, 1975)
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(2000). "Examining computational geometry, vanEmdeBoastrees, and hashing from the perspective of the fusion tree". SIAM Journal on Computing. 29 (3): 1030–1049...
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any?)." Semantics and Contextual Expression, ed. by Bartsch, van Benthem, and vanEmdeBoas. Foris, 294–318. Szabolcsi, Anna (1992), "Combinatory grammar...
1983 by Hendrik Lenstra, combining ideas by László Lovász and Peter vanEmdeBoas. Doignon's theorem asserts that an integer program is feasible whenever...
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