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Topic: Minimum spanning tree

Related Topics

Minimal spanning tree

Spanning tree (mathematics)

Euclidean minimum spanning tree

Steiner tree

Undirected graph

List of algorithms

Connected graph

Graph theory

Shortest path problem

Traveling salesman problem

Eulerian path

Algorithm

Biadjacency matrix

Adjacency matrix

Clique problem

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	PlanetMath: minimum spanning tree
		with weighted edges, a minimum spanning tree is a spanning tree with minimum weight, where the weight of a spanning tree is the sum of the weights of its edges.
		There may be more than one minimum spanning tree for a graph, since it is the weight of the spanning tree that must be minimum.
		This is version 4 of minimum spanning tree, born on 2002-02-25, modified 2004-03-28.
	planetmath.org /encyclopedia/MinimumSpanningTree.html (0 words)

	A Weighted Coding in a Genetic Algorithm for the Degree-Constrained Minimum Spanning Tree Problem
		On a set of hard graphs whose unconstrained minimum spanning trees are of high degree, a steady-state GA that uses the weighted coding identifies degree-constrained spanning trees that are on average shorter than those found by several competing algorithms.
		Patterns of symbols do not represent consistent substructures of spanning trees, so that crossover may generate offspring whose trees do not resemble the trees of their parents, and the mutation of even one symbol may change the represented tree radically [23, 30].
		The weighted coding of spanning trees was implemented in an otherwise conventional steady-state GA. The algorithm selects chromosomes to be parents in tournaments of size three, and generates offspring from them via uniform crossover and a mutation that resets each gene to a new random value with a small probability (position-by-position mutation).
	www.acm.org /conferences/sac/sac2000/Proceed/FinalPapers/EC-11/www_wdmst.html (0 words)

	[No title] (Site not responding. Last check: )
		As a complementary analysis, a minimum spanning tree analysis was performed (Figure 3).
		The Minimum Spanning Tree (MST) histogram is a multivariate extension of the ideas behind the conventional scalar rank histogram.
		The use of scaled and de-biased MST histograms to diagnose attributes of ensemble forecasts is illustrated both for synthetic Gaussian ensembles and for a small sample of actual ensemble forecasts.
	www.lycos.com /info/minimum-spanning-tree.html (503 words)

	Cprogramming.com - Algorithms - Minimum Spanning Trees
		The idea behind minimum spanning trees is simple: given a graph with weighted edges, find a tree of edges with the minimum total weight.
		It's probably easiest to understand a tree using the definition that a tree is both connected and acyclic; think about binary trees--every node in the tree is reachable, so it's connected, and there are no cycles because you can't go back up the tree.
		The closest vertex to the minimum spanning tree should then be added to the tree, and the process of checking its neighbors to see if they can reach the tree more quickly via the new vertex than any other vertex in the tree should be repeated.
	cprogramming.com /tutorial/computersciencetheory/mst.html (0 words)

	Lecture 17 - minimum spanning trees
		Minimum spanning tree is always taught in algorithm courses since (1) it arises in many applications, (2) it is an important example where greedy algorithms always give the optimal answer, and (3) Clever data structures are necessary to make it work.
		Minimum spanning trees are useful in constructing networks, by describing the way to connect a set of sites using the smallest total amount of wire.
		is a subset of a minimum spanning tree.
	www2.toki.or.id /book/AlgDesignManual/LEC/LECTUR16/NODE17.HTM (0 words)

	Mazes
		Any connected graph has a spanning tree, i.e., a tree which is a subgraph with exactly same vertices but only some of the edges.
		The resulting tree is known as the minimum spanning tree.
		the graph is bound to be a tree that contains all the vertices of the given graph and, therefore, serves as its spanning tree.
	www.cut-the-knot.org /ctk/Mazes.shtml (0 words)

	CS174 Spring 99, Lecture 19 Summary, John Canny
		Remember the minimum spanning tree problem – you are given a graph G with weighted edges (real values on each edge) and the goal is to find a spanning tree T whose total weight is minimal.
		Minimum spanning trees are useful for planning computer networks and for certain other kinds of resource and layout problems.
		Because we can delete all the F-heavy edges in G without changing the spanning tree of G, (even though F is the spanning forest for a subgraph of G) we can reduce the spanning tree calculation for G to a spanning tree calculation for a graph with a linear number of edges (n/p).
	www.cs.berkeley.edu /~jfc/cs174lecs/lec19/lec19.html (0 words)

	Minimum Spanning Tree
		Minimum spanning tree is only one of several spanning tree problems that arise in practice.
		A recent breakthrough on the minimum spanning tree problem is the linear-time randomized algorithm of Karger, Klein, and Tarjan [KKT95].
		Minimum spanning tree algorithms have an interpretation in terms of matroids, which are systems of subsets closed under inclusion, for which the maximum weighted independent set can be found using a greedy algorithm.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE161.HTM (0 words)

	Cprogramming.com - Algorithms - Minimum Spanning Trees
		The idea behind minimum spanning trees is simple: given a graph with weighted edges, find a tree of edges with the minimum total weight.
		It's probably easiest to understand a tree using the definition that a tree is both connected and acyclic; think about binary trees--every node in the tree is reachable, so it's connected, and there are no cycles because you can't go back up the tree.
		The closest vertex to the minimum spanning tree should then be added to the tree, and the process of checking its neighbors to see if they can reach the tree more quickly via the new vertex than any other vertex in the tree should be repeated.
	www.cprogramming.com /tutorial/computersciencetheory/mst.html (692 words)

	Transform - Spanning Tree (Site not responding. Last check: )
		spanning tree connects points so that if the lengths of all the links are added up there is no way to connect all of the points using links with a lower total length.
		The minimum spanning tree transform simply guarantees that no tree can be drawn that uses less material than the spanning tree it finds.
		Minimum spanning trees are very important in a very wide range of disciplines.
	www.manifold.net /doc/7x/transform_spanning_tree.htm (451 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: )
		Given a connected, undirected graph, a spanning tree of that graph is a subgraph which is a tree and connects all the vertices together.
		A minimum spanning tree or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree.
		A related graph is the k-minimum spanning tree">k-minimum spanning tree (k-MST) which is the tree that spans some subset of k vertices in the graph with minimum weight.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Minimum_spanning_tree (969 words)

	R: Minimum spanning tree
		A subgraph of a connected graph is a minimum spanning tree if it is tree, and the sum of its edge weights are the minimal among all tree subgraphs of the graph.
		A minimum spanning forest of a graph is the graph consisting of the minimum spanning trees of its components.
		A graph object with the minimum spanning forest.
	cneurocvs.rmki.kfki.hu /igraph/doc/R/minimum.spanning.tree.html (0 words)

	Minimum Spanning Tree of Urban Tapestries messages at Mauro Cherubini’s moleskine
		Recently I managed to calculate the Minimum Spanning Tree (MST) of the Urban Tapestries dataset that was collected during the trial of 2004.
		Given a connected, undirected graph, a spanning tree of that graph is a subgraph which is a tree and connects all the vertices together.
		For the Urban Tapestries dataset, I had to adapt a version of Kruskal’s algorithm for minimum spanning trees that was greatly implemented by Prof.
	www.i-cherubini.it /mauro/blog/2006/04/06/minimum-spanning-tree-of-urban-tapestries-messages (367 words)

	Class notes CS251B -- Winter 1997
		Spanning tree: a free tree on V (thus having V-1 edges that are a subset ofE).
		Minimum Spanning tree: the spanning tree with minimal total weight, where the weights of the edges picked are summed to obtain a total weight..
		In this graph, the red lines are the minimum spanning tree and the fl lines are the edges which exist but are not part of the minimum spanning tree..
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic28 (0 words)

	Spanning Tree Relaxation
		Assuming that all of the costs are nonnegative, the optimal tour must be at least as long as that for the minimum spanning tree.
		Therefore the minimum spanning tree is cheaper than the cheapest tour.
		The minimum spanning tree for our example is in figure 1.
	mat.gsia.cmu.edu /mstc/relax/node4.html (0 words)

	Minimum spanning tree (Site not responding. Last check: )
		A minimum spanning tree is a tree formed from a subset of theedges in a given undirected graph, with two properties:
		The first algorithm for finding a minimum spanning tree was developed by Czech scientist Otakar Borůvka in 1926(see Boruvka's algorithm).
		The fastest minimum spanning tree algorithm to date was developed by Chazelle, and based on Borůvka's.
	www.therfcc.org /minimum-spanning-tree-11124.html (406 words)

	Undirected Graphs and Minimum Spanning Trees
		The Minimum Spanning Tree of an Undirected Graph
		An unrooted tree can be made into a rooted tree: If the unrooted tree is "floppy" and it is "picked up" by a leaf to make a root, the new root has one child, every internal vertex has at least one child, and every (other) leaf has no children.
		Kruskal's algorithm certainly leads to a spanning tree T but it is necessary to prove that T is minimal.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph/Undirected (0 words)

	American Mathematical Society :: Feature Column
		The goal is to try to find a spanning tree of the graph which has the property that the sum of the weights of the edges in the tree is a minimum.
		The meaning of being a spanning tree is that the tree includes all of the vertices of the original graph.
		In this model we seek that spanning tree of the original graph such that the sum of the weights on the edges of the spanning tree T together with the sum of the weights at the vertices of T is a minimum.
	www.ams.org /featurecolumn/archive/trees.html (4709 words)

	Minimum Spanning Trees
		A minimum spanning tree is the same as any other fully connected graph, except that each of the edges (not paths) is minimal.
		The minimum spanning tree is the (minimal, in terms of cost) set of edges required to join the graph.
		Clearly, this is not a minimum spanning tree.
	student-nt.wou.edu /JCM/CS313/MST.htm (656 words)

	[No title]
		This is because G will have at least one spanning tree (just remove edges of G one at a time until all cycles have been removed but the vertices are still connected).
		In fact, we could list all possible spanning trees of G. Then a minimum spanning tree is any one of these trees which has minimal weight.
		Suppose E1 is a subset of E with the property that E1 is a subset of the edges in a minimal spanning tree T for G. Let V1 be the set of vertices incident with edges in E1.
	www.ececs.uc.edu /~cpurdy/lec21.html (0 words)

	Rectilinear Minimum Spanning Tree Demonstration Applet - John A. Nestor
		Prim's Algorithm operates incrementally on a partial tree starting with a single terminal - on each iteration, it adds an edge between the partial tree and the terminal that is closest to any terminal in the partial tree.
		Given a set of terminal points in a plane, a rectilinear minimum spanning tree is a set of edges which connects all the terminals with minimum rectilinear distance.
		The RMST Problem is a special case of the Minimum Spanning Tree problem studied in Computer Science Algorithms textbooks in that the distances between the points imply a complete graph.
	foghorn.cadlab.lafayette.edu /cadapplets/STree/RMSTApplet.html (0 words)

	Test datasets for the Minimum Labeling Spanning Tree problem
		Given a set of communication network nodes, the problem is to find a spanning tree (a connected communication network) that uses as few types of communication lines as possible.
		The objective is to find a spanning tree which uses the smallest number of different types of edges.
		The aim is to find a spanning tree of the graph using the minimum number of colors, which means that all the terminal nodes are required to be covered avoiding cycles and minimizing the overall number of different companies.
	people.brunel.ac.uk /~mapgssc/MLSTP.htm (0 words)

	minimum_spanning_tree(+Graph, +DistanceArg, -Tree, -TreeWeight) (Site not responding. Last check: )
		A minimum spanning tree is a smallest subset of the graph's edges that still connects all the graph's nodes.
		Such a tree is not unique and of course exists only if the original graph is itself connected.
		The computed tree is returned in Tree, which is simply a list of the edges that form the tree.
	www.cs.waikato.ac.nz /~jcleary/222/eclipsedoc/bips/lib/graph_algorithms/minimum_spanning_tree-4.html (265 words)

	Greedy Algorithms
		Little more formally, a spanning tree of a graph G is a subgraph of G that is a tree and contains all the vertices of G. An edge of a spanning tree is called a branch; an edge in the graph that is not in the spanning tree is called a chord.
		(MST) of a weighted graph G is a spanning tree of G whose edges sum is minimum weight.
		So n-1 is the minimum number of edges in the T. Hence if G` is connected and T has more that n-1 edges, we can remove at least one of these edges without disconnecting (choose an edge that is part of cycle).
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/Greedy/mst.htm (0 words)

	Generic Minimum Spanning Tree
		Informally, the MST problem is to find a free tree T of a given graph G that contains all the vertices of G and has the minimum total weight of the edges of G over all such trees.
		The problem of constructing a minimum spanning tree of MST is computing a spanning tree T with smallest total weight.
		As we have mentioned, an MST shows the most economical way of connecting all vertices of weighted graph together using the edges of the graph.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/GraphAlgor/genericMST.htm (0 words)

	Page 57
		The MST is the tree of minimum length connecting the objects, where by 'length' I mean the sum of the weights of the connecting links in the tree.
		Whether we are interested in a minimum or maximum spanning tree depends entirely on the application we have in mind.
		It is interesting that the MST has, independently of their work, been used to reduce storage when storing object descriptions, which amounts to a practical application of their result[53].
	www.dcs.gla.ac.uk /~iain/keith/data/pages/57.htm (0 words)

	Minimum spanning trees
		A less obvious application is that the minimum spanning tree can be used to approximately solve the traveling salesman problem.
		Christofides' heuristic) of using minimum spanning trees to find a tour within a factor of 1.5 of optimal; I won't describe this here but it might be covered in ICS 163 (graph algorithms) next year.
		Prim's algorithm then builds one large tree by connecting it with the small trees in the list L built by Boruvka's algorithm, keeping a heap which stores, for each tree in L, the best edge that can be used to connect it to the large tree.
	www.ics.uci.edu /~eppstein/161/960206.html (0 words)

	Graphs: Minimum Cost Spanning Tree
		A spanning tree for G is a free tree that connects all vertices in G. A connected acyclic graph is also called a free tree.
		The cost of the spanning tree is the sum of the cost of all edges in the tree.
		The algorithm adds nodes to the spanning tree one at a time, in order of the edge cost to connect to the nodes already in the tree.
	www.cs.rochester.edu /users/faculty/nelson/courses/csc_173/graphs/mcst.html (0 words)

	MINIMUM UPGRADING SPANNING TREE
		), a threshold value D for the weight of a minimum spanning tree.
		of vertices such that the weight of a minimum spanning tree in G with respect to edge weights given by
		Comment: Variation in which the upgrading set must be chosen such that the upgraded graph contains a spanning tree in which no edge has weight greater than D is approximable within
	www.nada.kth.se /~viggo/wwwcompendium/node83.html (143 words)

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