A. Frieze and T. Johansson, "On edge disjoint spanning trees in a randomly weighted complete graph," arXiv preprint arXiv:1505.03429, 2015.Flaxman, A. D., Vera, J., and Frieze, A. M. On edge-disjoint spanning trees in a randomly weighted complete graph. Manuscript in preparation, ...
We give a simple sufficient condition for a weighted graph to have a diameter-preserving spanning tree. More precisely, let G =(V, E, f E ) be a connected edge weighted graph with f E being the edge weight function. Let f V be the vertex weight function of G induced by f E as ...
A prototypical example is the kMST problem in which we require a tree of minimum weight spanning at least k nodes in an edge-weighted graph. We show that the kMST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio 2 root k...
Spanning trees only exist for connected graphs. Otherwise, a spanning tree exists for each connected component. All spanning trees of a graph have the same number of edges. Negative weights can be avoided by adding a constant to all weights. Maximum spanning tree can be obtained with w′(e)...
Spanning Trees and Shortest Paths in Monge Graphs* T. Dudfis and R. Rudolf, Graz We investigate three problems on Monge graphs, i.e. complete, undirected weighted graphs whose distance matrix is a Monge matrix: (A) the minimum spanning tree problem, (B) the problem of computing all-pairs...
Let’s see this in steps with an example graph: Step 0: create a graph Step 1: start with a bunch of unconnected trees (number of trees = number of vertices) Step 2: while there are unconnected trees, for each unconnected tree: ...
A similar exchange technique is used to construct the computation tree for a directed graph in O ( NV + V 3 ) time. The time for listing out the trees remains O ( N ). For a weighted graph, we show how to sort the spanning trees by weight using the computation tree in O ( N ...
In this study a novel approach to graph-theoretic clustering is presented. A clustering algorithm which uses a structure called scale-free minimum spanning... Niina Paeivinen - 《Pattern Recognition Letters》 被引量: 163发表: 2005年 Optimal Path and Minimal Spanning Trees in Random Weighted Netwo...
To obtain the Maximum Spanning Tree of a Graph represented by undirected weighted graph using Prim’s Algorithm , is the objective. Prims algorithm " is a tool that helps to determine the Minimum and Maximum Spanning Trees ( Greedy algorithm ) in a Graph ( Tree (MST ). ...
In certain fields of graph theory it is often useful to find a minimum spanning tree of a weighted graph. Other optimization problems on spanning trees have also been studied, including the maximum spanning tree, the minimum tree that spans at least k vertices, the minimum spanning tree with ...