mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

, a random tree is a

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...

or arborescence that is formed by a

stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...

. Types of random trees include: *

Uniform spanning tree A uniform is a variety of clothing worn by members of an organization while participating in that organization's activity. Modern uniforms are most often worn by armed forces and paramilitary organizations such as police, emergency services, s ...

, a spanning tree of a given graph in which each different tree is equally likely to be selected *

Random minimal spanning tree In mathematics, a random minimum spanning tree may be formed by assigning random weights from some distribution to the edges of an undirected graph, and then constructing the minimum spanning tree of the graph. When the given graph is a complete gr ...

, spanning trees of a graph formed by choosing random edge weights and using the minimum spanning tree for those weights *

Random binary tree In computer science and probability theory, a random binary tree is a binary tree selected at random from some probability distribution on binary trees. Two different distributions are commonly used: binary trees formed by inserting nodes one at ...

, binary trees with a given number of nodes, formed by inserting the nodes in a random order or by selecting all possible trees uniformly at random *

Random recursive tree In probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices. Definition and generation In a recursive tree with n vertices, the vertices are labeled by the num ...

, increasingly labelled trees, which can be generated using a simple stochastic growth rule. *

Treap In computer science, the treap and the randomized binary search tree are two closely related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys. After any sequence of in ...

or randomized binary search tree, a data structure that uses random choices to simulate a random binary tree for non-random update sequences * Rapidly exploring random tree, a fractal space-filling pattern used as a data structure for searching high-dimensional spaces *

Brownian tree In probability theory, the Brownian tree, or Aldous tree, or Continuum Random Tree (CRT) is a special case from random real trees which may be defined from a Brownian excursion. The Brownian tree was defined and studied by David Aldous in three a ...

, a fractal tree structure created by diffusion-limited aggregation processes *

Random forest Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. For classification tasks, the output of th ...

, a machine-learning classifier based on choosing random subsets of variables for each tree and using the most frequent tree output as the overall classification *

Branching process In probability theory, a branching process is a type of mathematical object known as a stochastic process, which consists of collections of random variables. The random variables of a stochastic process are indexed by the natural numbers. The origi ...

, a model of a population in which each individual has a random number of children

External links

* {{set index article Trees (graph theory) Probabilistic data structures Random graphs

See also

External links