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Consider a directed graph, G(N,A), where N and A are the set of nodes and arcs, respectively. Associated with each arc (i,j) in A is a cost c(i,j). Let N=n and A=m. The problem is to find a rooted directed spanning tree, G(N,S) where S is a subset of A such that the sum of c(i,j) for all (i,j) in S is minimized. The rooted directed spanning tree is defined as a graph which connects, without any cycle, all nodes with n1 arcs, i.e., each node, except the root, has one and only one incoming arc.
The Directed Minimum Spanning Tree Problem
ChuLiu/Edmonds Algorithm
A Linear Algorithm for Analysis of Minimum Spanning and..  Booth, Westbrook (1992) (9 citations) (Correct)
....list. We call this embedding dependent depthfirst search topological. Figure 1 gives an example of an embedded planar graph and spanning tree with preorder and postorder numbering. We denote the preorder and postorder numbers of v by pre(v) and post(v) respectively. It is well known (see e.g. [17]) that for any pair u and v of vertices, v is an ancestor of u if and only if pre(v) pre(u) and post(u) post(v) Let f be a non tree edge fu; vg. We denote by nca(f) the nearest common ancestor of u and v. Edge f is a potential critical edge for every vertex on the tree path connecting u and v, ....
R. E. Tarjan. Finding dominators in directed graphs. SIAM J. Comput., 3, 1974.
Graph Theory Lecture Notes 16 Minimum Spanning Trees
Design and Analysis of Computer Algorithms
minimum spanning tree algorithms Kruskal and Prim algorithms covered.
Data Structures and Algorithms Graph Algorithms 10.1 Minimum Spanning Trees
Suppose we have a group of islands that we wish to link with bridges so that it is possible to travel from one island to any other in the group. Further suppose that (as usual) our government wishes to spend the absolute minimum amount on this project (because other factors like the cost of using, maintaining, etc, these bridges will probably be the responsibility of some future government :). The engineers are able to produce a cost for a bridge linking each possible pair of islands. The set of bridges which will enable one to travel from any island to any other at minimum capital cost to the government is the minimum spanning tree.
MinimumCost Spanning Trees
... The minimal subgraph of a connected graph is called a spanning tree: Definition
...
Figure: An undirected graph and three spanning trees. According ...
www.brpreiss.com/books/opus5/html/page573.html  11k 
Minimum Spanning Trees
... point set defines a complete graph, with edge assigned a weight equal to the distance
from to . Additional applications of minimum spanning trees are discussed ...
www2.toki.or.id/book/ AlgDesignManual/BOOK/BOOK2/NODE73.HTM  8k 
[ More results from www2.toki.or.id
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Minimum Spanning Tree  from MathWorld
Minimum Spanning Tree. The minimum spanning tree of a weighted graph
is a set of
edges of minimum total weight which form a spanning tree of the graph. ...
mathworld.wolfram.com/MinimumSpanningTree.html  19k 
Spanning Tree  from MathWorld
... A count of the spanning trees of a graph can be found using the command
NumberOfSpanningTrees[g] in the Mathematica addon package DiscreteMath`Combinatorica ...
mathworld.wolfram.com/SpanningTree.html  20k Cached  Similar pages
Science Fair
Projects  Minimum spanning tree
... tree and connects all the vertices together. A single graph can have many
different spanning trees. We can also assign a weight to ...
www.allsciencefairprojects.com/science_ fair_projects_encyclopedia/Minimum_spanning_tree
 17k 
1.4.3 Minimum Spanning Tree
... The Algorithm Design Manual: The minimum spanning tree (MST) of a graph
defines
the cheapest subset of edges that keeps the graph in one connected component. ...
www.cs.sunysb.edu/~algorith/ files/minimumspanningtree.shtml  5k  Oct 31, 2004 
Definition of Spanning tree (mathematics)
... Cayley's theorem can be used to find the number of labelled spanning trees in a
complete graph. There are exactly n power(n2) labelled trees with n vertices. ...
www.wordiq.com/definition/Spanning_tree_(mathematics)  10k 
[PDF]
7.2. Spanning Trees
7.2.1. Spanning Trees. A tree T is a spanning ...
File Format: PDF/Adobe Acrobat 
View as HTML
... Spanning tree. Every connected graph has a spanning tree which can be obtained
by removing edges until the resulting graph becomes acyclic. ...
www.math.northwestern.edu/~mlerma/ courses/cs310/notes/dmspanning.pdf 
Undirected Graphs and Minimum Spanning
Trees
The Minimum Spanning Tree of an Undirected Graph. ... It repeatedly joins two
trees
together until a spanning tree of the entire given graph remains. ...
www.csse.monash.edu.au/ ~lloyd/tildeAlgDS/Graph/Undirected/  31k 
Info on Spanning Trees of a Connected
Graph
... The tree graph of G, denoted T(G), is the graph whose vertices are the
spanning
trees of G and whose edges join those spanning trees that differ by an edge ...
www.theory.csc.uvic.ca/~cos/inf/subg/Spanning.html  6k  Oct 31, 2004 
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