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In graph theory, a tree is an undirected graph in which any two vertices ... 1997), The Art of Computer Programming Volume 1: Fundamental Algorithms (3rd ed ...
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
For general graphs, the best known algorithms for both undirected and directed graphs is a simple greedy algorithm: In the undirected case, the greedy tour is at most O(ln n)-times longer than an optimal tour. [1] The best lower bound known for any deterministic online algorithm is 10/3. [2]
Treewidth is commonly used as a parameter in the parameterized complexity analysis of graph algorithms. Many algorithms that are NP-hard for general graphs, become easier when the treewidth is bounded by a constant. The concept of treewidth was originally introduced by Umberto Bertelè and Francesco Brioschi under the name of dimension.
This tree is known as a depth-first search tree or a breadth-first search tree according to the graph exploration algorithm used to construct it. [18] Depth-first search trees are a special case of a class of spanning trees called Trémaux trees , named after the 19th-century discoverer of depth-first search.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
Girvan–Newman algorithm; Goal node (computer science) Gomory–Hu tree; Graph bandwidth; Graph edit distance; Graph embedding; Graph isomorphism; Graph isomorphism problem; Graph kernel; Graph neural network; Graph reduction; Graph traversal; GYO algorithm
In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex , where the total weight of all the edges in the tree is minimized.