Search results
Results From The WOW.Com Content Network
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]
It is easy to show that tree Y 2 is connected, has the same number of edges as tree Y 1, and the total weights of its edges is not larger than that of tree Y 1, therefore it is also a minimum spanning tree of graph P and it contains edge e and all the edges added before it during the construction of set V.
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.
It returns a spanning arborescence rooted at of minimum weight, where the weight of an arborescence is defined to be the sum of its edge weights, () = (). The algorithm has a recursive description. Let f ( D , r , w ) {\displaystyle f(D,r,w)} denote the function which returns a spanning arborescence rooted at r {\displaystyle r} of minimum weight.
Random minimum spanning tree on the same graph but with randomized weights. When the given graph is a complete graph on n vertices, and the edge weights have a continuous distribution function whose derivative at zero is D > 0 , then the expected weight of its random minimum spanning trees is bounded by a constant, rather than growing as a ...
Therefore, the k-minimum spanning tree must be formed by combining the optimal Steiner tree with enough of the zero-weight edges of the added trees to make the total tree size large enough. [2] Even for a graph whose edge weights belong to the set {1, 2, 3}, testing whether the optimal solution value is less than a given threshold is NP-complete.
A Euclidean minimum spanning tree, for a set of points in the Euclidean plane or Euclidean space, is a system of line segments, having only the given points as their endpoints, whose union includes all of the points in a connected set, and which has the minimum possible total length of any such system.
Example of a MST: The minimum spanning tree of a planar graph.Each edge is labeled with its weight, which here is roughly proportional to its length. The distributed minimum spanning tree (MST) problem involves the construction of a minimum spanning tree by a distributed algorithm, in a network where nodes communicate by message passing.