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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 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 trees achieve optimal asymptotic complexity on some operations. They have mainly theoretical importance.
An exponentialtree is a type of search tree where the number of children of its nodes decreases doubly-exponentially with increasing depth. Values are...
sequence Exponential smoothing Exponential stability Exponential sum Exponential time Sub-exponential time ExponentialtreeExponential type Exponentially equivalent...
structure (Union-find data structure) Fusion tree Enfilade Exponentialtree Fenwick tree Van Emde Boas tree Rose tree These are data structures used for space...
an exponential. In this sense, problems that have sub-exponential time algorithms are somewhat more tractable than those that only have exponential algorithms...
structure's O(logw n) runtime in expectation. Another dynamic version using exponentialtree was proposed in 2007 which yields worst-case runtimes of O(logw n +...
combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures...
hierarchical data as a tree suffers from visual clutter as the number of nodes per level can grow exponentially. For a simple binary tree, the maximum number...
updates, where w is the word size. Fusion trees use O(n) space and can be made dynamic with hashing or exponentialtrees. There is a verified implementation...
then the minimum spanning tree of the weighted graph is constructed. Because a graph may have exponentially many spanning trees, it is not possible to list...
In computer science, Monte Carlo tree search (MCTS) is a heuristic search algorithm for some kinds of decision processes, most notably those employed in...
Saurabh, Saket (2015). "Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree". Automata, Languages, and Programming – 42nd...
= RL problem Unique games conjecture Is the exponential time hypothesis true? Is the strong exponential time hypothesis (SETH) true? Do one-way functions...
(1986). In Chapter 4, Engines Of Abundance, Drexler illustrates both exponential growth and inherent limits (not gray goo) by describing "dry" nanomachines...
has limited value in a fault tree. Quite often, Poisson-Exponentially distributed rates are used to quantify a fault tree instead of probabilities. Rates...
in T p M {\displaystyle T_{p}M} , the curve defined by the Riemannian exponential map, γ ( t ) = exp p ( t v ) {\displaystyle \gamma (t)=\exp _{p}(tv)}...
complexity the decision tree model is the model of computation in which an algorithm is considered to be basically a decision tree, i.e., a sequence of queries...
In computer science, an exponential search (also called doubling search or galloping search or Struzik search) is an algorithm, created by Jon Bentley...
children, at an exponentially distributed time after its first appearance as an external node. The number of external nodes in the tree, at any time, is...
versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special...
better than the exponential time required for a brute-force search, it is still too slow to be practical when the number of elements in the tree is very large...
types of generating functions, including ordinary generating functions, exponential generating functions, Lambert series, Bell series, and Dirichlet series;...
mistake the logistic function (S-function) for an exponential function, and to see a "knee" in an exponential function where there can in fact be no such thing...