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An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
Given an undirected tree presented as a set of edges, the Euler tour representation (ETR) can be constructed in parallel as follows: We construct a symmetric list of directed edges: For each undirected edge {u,v} in the tree, insert (u,v) and (v,u) in the edge list. Sort the edge list lexicographically. (Here we assume that the nodes of the ...
The time complexity of operations in the adjacency list representation can be improved by storing the sets of adjacent vertices in more efficient data structures, such as hash tables or balanced binary search trees (the latter representation requires that vertices are identified by elements of a linearly ordered set, such as integers or ...
A simple implementation of Prim's, using an adjacency matrix or an adjacency list graph representation and linearly searching an array of weights to find the minimum weight edge to add, requires O(|V| 2) running time.
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees.
This simple model is commonly known as the adjacency list model and was introduced by Dr. Edgar F. Codd after initial criticisms surfaced that the relational model could not model hierarchical data. [citation needed] However, the model is only a special case of a general adjacency list for a graph.
The Nested Set model is appropriate where the tree element and one or two attributes are the only data, but is a poor choice when more complex relational data exists for the elements in the tree. Given an arbitrary starting depth for a category of 'Vehicles' and a child of 'Cars' with a child of 'Mercedes', a foreign key table relationship must ...
A binary tree can be implemented as a list of lists: the head of a list (the value of the first term) is the left child (subtree), while the tail (the list of second and subsequent terms) is the right child (subtree).