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If the graph is connected, it finds a minimum spanning tree. It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle. [2] The key steps of the algorithm are sorting and the use of a disjoint-set data structure to detect cycles. Its running time is dominated by the time to sort all of the ...
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.
The junction tree algorithm (also known as 'Clique Tree') is a method used in machine learning to extract marginalization in general graphs. In essence, it entails performing belief propagation on a modified graph called a junction tree .
It matters little whether the list of walls is initially randomized or if a wall is randomly chosen from a nonrandom list, either way is just as easy to code. Because the effect of this algorithm is to produce a minimal spanning tree from a graph with equally weighted edges, it tends to produce regular patterns which are fairly easy to solve.
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
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]
In graph theory, Edmonds' algorithm or Chu–Liu/Edmonds' algorithm is an algorithm for finding a spanning arborescence of minimum weight (sometimes called an optimum branching). [1] It is the directed analog of the minimum spanning tree problem.
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. [2]