spanning tree algorithm - ορισμός. Τι είναι το spanning tree algorithm
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Τι (ποιος) είναι spanning tree algorithm - ορισμός

DATA STRUCTURE, SUBGRAPH OF A WEIGHTED GRAPH
Spanning tree algorithm; Minimal spanning tree; Shortest spanning tree; Minimum spanning forest; Minimum weight spanning tree; Minimum weight spanning forest; Minimum cost spanning tree; Minimum Spanning Tree; Minimum spanning tree problem; Spanning tree problem; Minimum k-node-connected spanning network problem; Minimum k-edge-connected spanning network problem; Minimum Weight Spanning Tree; Minimum spanning trees; Min spanning tree; Parallel algorithms for the minimum spanning tree problem; Algorithms for finding minimum spanning trees; Applications of the minimum spanning tree problem; Applications of minimum spanning trees
  • A [[planar graph]] and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length.
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  • This figure shows there may be more than one minimum spanning tree in a graph. In the figure, the two trees below the graph are two possibilities of minimum spanning tree of the given graph.

spanning tree algorithm         
An IEEE 802.1 standard under consideration which will provide distributed routing over multiple LANs connected by bridges.
Minimum spanning tree         
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. That is, it is a spanning tree whose sum of edge weights is as small as possible.
Spanning tree         
  • A spanning tree (blue heavy edges) of a [[grid graph]]
  • [[Cayley's formula]] counts the number of spanning trees on a complete graph. There are <math>2^{2-2}=1</math> trees in <math>K_2</math>,
<math>3^{3-2}=3</math> trees in <math>K_3</math>, and <math>4^{4-2}=16</math>
trees in <math>K_4</math>.
SUBGRAPH OF AN UNDIRECTED GRAPH G THAT IS A TREE WHICH INCLUDES ALL OF THE VERTICES OF G
Spanning forest; Spanning Tree; Spanning tree (Mathematics); Spanning tree (networks); Spanning Tree (mathematics); Fundamental cycle; Fundamental cutset; Spanning tree (mathematics)
In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that is a tree which includes all of the vertices of G. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (see spanning forests below).

Βικιπαίδεια

Minimum spanning tree

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. That is, it is a spanning tree whose sum of edge weights is as small as possible. More generally, any edge-weighted undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of the minimum spanning trees for its connected components.

There are many use cases for minimum spanning trees. One example is a telecommunications company trying to lay cable in a new neighborhood. If it is constrained to bury the cable only along certain paths (e.g. roads), then there would be a graph containing the points (e.g. houses) connected by those paths. Some of the paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weights. Currency is an acceptable unit for edge weight – there is no requirement for edge lengths to obey normal rules of geometry such as the triangle inequality. A spanning tree for that graph would be a subset of those paths that has no cycles but still connects every house; there might be several spanning trees possible. A minimum spanning tree would be one with the lowest total cost, representing the least expensive path for laying the cable.