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Rooted trees, often with an additional structure such as an ordering of the neighbors at each vertex, are a key data structure in computer science; see tree data structure. In a context where trees typically have a root, a tree without any designated root is called a free tree. A labeled tree is a tree in which each vertex is given a unique label.
In graph theory and theoretical computer science, the level ancestor problem is the problem of preprocessing a given rooted tree T into a data structure that can determine the ancestor of a given node at a given distance from the root of the tree. More precisely, let T be a rooted tree with n nodes, and let v be an arbitrary node of T.
Viewed as a whole, a tree data structure is an ordered tree, generally with values attached to each node. Concretely, it is (if required to be non-empty): A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning: A directed graph,
A tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree , although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom.
An unrooted binary tree T may be transformed into a full rooted binary tree (that is, a rooted tree in which each non-leaf node has exactly two children) by choosing a root edge e of T, placing a new root node in the middle of e, and directing every edge of the resulting subdivided tree away from the root node. Conversely, any full rooted ...
Trees with a single root may be viewed as rooted trees in the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. In the first case, the graph is the undirected Hasse diagram of the partially ordered set, and in the second case, the graph is simply the underlying (undirected) graph of the ...
In graph theory, an arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly one directed walk from r to v (noting that the root r is unique). [1] An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph.
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees, clique trees, or join trees. They play an important role in problems like probabilistic inference ...