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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.
A minimum-cost spanning-forest game (MCSF game) is a generalization of an MCST game, in which multiple supply-nodes are allowed. In general, the core of an MCSF game may be empty. [ 1 ] However, if the underlying network is a tree, the core is always non-empty, and core points can be computed in strongly-polynomial time .
A minimum-cost spanning tree game is a cooperative game in which the players have to share among them the costs of constructing the optimal spanning tree. The optimal network design problem is the problem of computing a set, subject to a budget constraint, which contains a spanning tree, such that the sum of shortest paths between every pair of ...
An alternative model for generating spanning trees randomly but not uniformly is the random minimal spanning tree. In this model, the edges of the graph are assigned random weights and then the minimum spanning tree of the weighted graph is constructed. [25]
These algorithms find the minimum spanning forest in a possibly disconnected graph; in contrast, the most basic form of Prim's algorithm only finds minimum spanning trees in connected graphs. However, running Prim's algorithm separately for each connected component of the graph, it can also be used to find the minimum spanning forest. [9]
Capacitated minimum spanning tree is a minimal cost spanning tree of a graph that has a designated root node and satisfies the capacity constraint . The capacity constraint ensures that all subtrees (maximal subgraphs connected to the root by a single edge) incident on the root node r {\displaystyle r} have no more than c {\displaystyle c} nodes.
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). It is the directed analog of the minimum spanning tree problem.
The k-minimum spanning tree problem, studied in theoretical computer science, asks for a tree of minimum cost that has exactly k vertices and forms a subgraph of a larger graph. It is also called the k -MST or edge-weighted k -cardinality tree .