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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]
The quality of the tree is measured in the same way as in a graph, using the Euclidean distance between pairs of points as the weight for each edge. Thus, for instance, a Euclidean minimum spanning tree is the same as a graph minimum spanning tree in a complete graph with Euclidean edge weights.
t. e. The Spanning Tree Protocol (STP) is a network protocol that builds a loop-free logical topology for Ethernet networks. The basic function of STP is to prevent bridge loops and the broadcast radiation that results from them. Spanning tree also allows a network design to include backup links providing fault tolerance if an active link fails ...
Prim's 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. The algorithm operates by building this tree ...
For example, the minimum spanning tree of the graph associated with an instance of the Euclidean TSP is a Euclidean minimum spanning tree, and so can be computed in expected O(n log n) time for n points (considerably less than the number of edges). This enables the simple 2-approximation algorithm for TSP with triangle inequality above to ...
The general graph Steiner tree problem can be approximated by computing the minimum spanning tree of the subgraph of the metric closure of the graph induced by the terminal vertices, as first published in 1981 by Kou et al. [18] The metric closure of a graph G is the complete graph in which each edge is weighted by the shortest path distance ...
Minimum degree spanning tree; Minimum k-cut; Minimum k-spanning tree; Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in ...
In computer science, the minimum routing cost spanning tree of a weighted graph is a spanning tree minimizing the sum of pairwise distances between vertices in the tree. It is also called the optimum distance spanning tree, shortest total path length spanning tree, minimum total distance spanning tree, or minimum average distance spanning tree.