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Topic: Euclidean minimum spanning tree

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Minimum spanning tree

	NationMaster - Encyclopedia: Traveling salesman problem
		The length of the minimum spanning tree of the network is a natural lower bound for the length of the optimal route.
		The minimum spanning tree of a planar graph.
		Euclidean TSP, or planar TSP, is the TSP with the distance being the ordinary Euclidean distance.
	www.nationmaster.com /encyclopedia/Traveling-salesman-problem (3762 words)

	Minimum spanning tree - Encyclopedia, History, Geography and Biography
		The minimum spanning tree of a planar graph.
		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 related graph is the k-minimum spanning tree (k-MST) which is the tree that spans some subset of k vertices in the graph with minimum weight.
	www.arikah.com /encyclopedia/Minimum_spanning_tree (1038 words)

	Minimum spanning tree - Biocrawler
		Given a connected, undirected graph, a spanning tree of that graph is a subgraph which is a tree and connects all the vertices together.
		The fastest minimum spanning tree algorithm to date was developed by Bernard Chazelle, and based on Borůvka's.
		A related graph is the k-minimum spanning tree (k-MST) which is the tree that spans some subset of k vertices in the graph with minimum weight.
	www.biocrawler.com /encyclopedia/Minimum_weight_spanning_forest (649 words)

	Minimum spanning tree - Biocrawler
		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 spanning tree for that graph would be a subset of those paths that has no cycles but still connects to every house.
		A minimum spanning tree would be one with the lowest total cost.
	www.biocrawler.com /encyclopedia/Minimal_spanning_tree (649 words)

	Euclidean minimum spanning tree
		The most popular efficient algorithm for computing the EMST depends on the fact that its edges are a subset of the edges in every Delaunay triangulation of the points.
		An obvious application of Euclidean minimum spanning trees is to find the cheapest network of wires or pipes to connect a set of places, assuming the links cost a fixed amount per unit length.
		Another application of EMSTs is a constant-factor approximation algorithm for approximately solving the Euclidean traveling salesman problem, the version of the Traveling salesman problem on a set of points in the plane with edges labelled by their length.
	www.ufaqs.com /wiki/en/eu/Euclidean%20minimum%20spanning%20tree.htm (855 words)

	Euclidean minimum spanning tree . Delaunay triangulation
		The simplest algorithm to find an EMST, given n points, is to actually construct the complete graph on n vertices, which has n n - 1 edges, compute each edge weight by finding the distance between each pair of points, and then run a standard minimum spanning tree algorithm on it.
		spanning trees is to find the cheapest network of wires or pipes to connect a set of places, assuming the links cost a fixed amount per unit length.
		The Euclidean minimum spanning tree or EMST is a minimum spanning tree of a set of points in the plane mathematics plane or more generally in \Bbb ^n, where the weight of the edge between each pair of points is the distance between those two points.
	www.uk.kunsimuna.net /Euclidean_minimum_spanning_tree_UK_862688_uc (716 words)

	Euclidean minimum spanning tree - Education - Information - Educational Resources - Encyclopedia - Music
		The Euclidean minimum spanning tree or EMST is a minimum spanning tree of a set of points in the plane, where the weight of the edge between each pair of points is the distance between those two points.
		The simplest algorithm to find an EMST, given n points, is to actually construct the complete graph on n vertices, which has n(n - 1) edges, compute each edge weight by finding the distance between each pair of points, and then run a standard minimum spanning tree algorithm on it.
		Another application of EMSTs is to approximating the Traveling Salesman Problem on a set of points obeying the triangle inequality, such as a set of points in the plane.
	education.music.us /E/Euclidean-minimum-spanning-tree.htm (1127 words)

	The Dispatch - Serving the Lexington, NC - News
		More generally, any undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of minimum spanning trees for its connected components.
		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.
		A set of k-smallest spanning trees is a subset of k spanning trees (out of all possible spanning trees) such that no spanning tree outside the subset has smaller weight.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Minimum_spanning_tree (1252 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)

	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..
		Euclidean MST's (EMST's) are utilized in the event of the need to find an MST of a number of nodes in Euclidean space, where each node is actually a vector.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic28 (1859 words)

	Probability and Algorithms
		The restrictions that this theorem imposes on a Euclidean functional are as few as one can reasonably expect to yield a generally useful limit theorem, and because of this generality the restriction to uniformly distributed random variables is palatable.
		Let t2 be the tree consisting of the vertex ξ1 and the vertex that is closest to ξ1 in Euclidean distance, together with the edge (straight line segment) connecting ξ1 and ξ2.
		It is natural to conjecture that is itself a tree with probability 1, but this possibility seems to be related to deep issues in continuum percolation, and the introduction of permits one to finesse that subtle issue.
	books.nap.edu /openbook.php?record_id=2026&page=109 (6365 words)

	Steiner Tree
		Many different phylogenic tree construction algorithms have been developed, which vary in the data they attempt to model and what the desired optimization criterion is. Because they all give different answers, identifying the correct algorithm for a given application is somewhat a matter of faith.
		The worst case for a minimum spanning tree approximation of the Euclidean distance problem is three points forming an equilateral triangle.
		Euclidean Steiner tree is not known to be in NP, because of numerical issues in representing distances.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE181.HTM (1383 words)

	Steiner tree (Site not responding. Last check: )
		A Steiner tree is a subtree of G that connects the terminals with the minimum total length (sum of all lengths of edges in the tree).
		The main difference is that, in the minimum spanning tree problem, we are looking for a tree that connects all vertices of G. In Steiner tree problem, we only have to connect the terminals.
		One common approximation to the Steiner tree problem is to compute the Euclidean minimum spanning tree.
	www.askfactmaster.com /Steiner_tree (144 words)

	Methods and apparatus for inferring orientation of lines of text - Patent 5664027
		The objective is to construct a Euclidean minimum spanning tree from the fully connected graph.
		A spanning tree is a Euclidean minimum spanning tree if the edges in the spanning tree are such that the sum of the distances which the edges represent is the minimum possible such sum.
		Further, while a preferred embodiment of the techniques constructs a Euclidean minimum spanning tree and determines the orientation of the lines from the edges of the Euclidean minimum spanning tree, other techniques may be used to define graphs from which the orientation of the lines may be determined.
	www.freepatentsonline.com /5664027.html (6587 words)

	BioMed Central \| Full text \| An interactive visualization tool to explore the biophysical properties of amino acids and ...
		In our application, this is most likely to be useful when users request a spanning tree for a large set of amino acid indices, under which conditions the force-based layout may become stuck at a local optimum, visible to the user as a representation in which one or a few key edges cross one another.
		Although this minimum spanning tree emphasizes the legitimacy of treating Polar Requirement as a measure of hydrophobicity (its authors originally introduced the metric as an estimate of stereic affinities between nucleotides and amino acids [36]), the tri-partite spanning tree for the concept of hydrophobicity illustrates the potential dangers of over-emphasizing any one measure of hydrophobicity.
		Specifically, the spanning tree of size, charge, and hydrophobicity (Figure 2) is recolored to indicate whether each amino acid index is more highly correlated with the PAM74-100 amino acid substitution matrix (green) or a matrix of amino acids' proximity within the standard genetic code [8] (brown).
	www.biomedcentral.com /1471-2105/7/329 (3815 words)

	News \| TimesDaily.com \| TimesDaily \| Florence, Alabama (AL)
		The Steiner tree problem is superficially similar to the minimum spanning tree problem: given a set V of points (vertices), interconnect them by a network (graph) of shortest length, where the length is the sum of the lengths of all edges.
		The difference between the Steiner tree problem and the minimum spanning tree problem is that, in the Steiner tree problem, extra intermediate vertices and edges may be added to the graph in order to reduce the length of the spanning tree.
		The metric Steiner tree problem corresponds to the Steiner tree in graphs problem where the graph has an infinite number of vertices, which are all points of the metric space.
	www.timesdaily.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Steiner_tree (472 words)

	Emst \| English \| Dictionary & Translation by Babylon
		EMST is also an acronym for Euclidean minimum spanning tree.
		Emst is a town of 3,000 inhabitants, located in the municipality of Epe in the province of Gelderland in the Netherlands.
		The Euclidean minimum spanning tree or EMST is a minimum spanning tree of a set of points in the plane (or more generally in), where the weight of the edge between each pair of points is the distance between those two points.
	www.babylon.com /definition/Emst (162 words)

	David Eppstein - Publications
		Includes proofs of several bounds on triangulation weight relative to the minimum spanning tree or non-Steiner triangulation, and a conjecture that for convex polygons the only points that need to be added are on the polygon boundary.
		The method is to use a minimum spanning tree to find a collection of overlapping circles, then shrink them one by one to reduce the number of overlaps, using Sleator and Tarjan's dynamic tree data structure to keep track of the connectivity of the shrunken circles.
		We describe algorithms for maintaining the minimum spanning tree in a graph in which the edge weights are piecewise linear functions of time that may change unpredictably.
	www.ics.uci.edu /~eppstein/pubs/mst.html (1477 words)

	Probability and Algorithms
		The restrictions that this theorem imposes on a Euclidean functional are as few as one can reasonably expect to yield a generally useful limit theorem, and because of this generality the restriction to uniformly distributed random variables is palatable.
		Let t2 be the tree consisting of the vertex ξ1 and the vertex that is closest to ξ1 in Euclidean distance, together with the edge (straight line segment) connecting ξ1 and ξ2.
		It is natural to conjecture that is itself a tree with probability 1, but this possibility seems to be related to deep issues in continuum percolation, and the introduction of permits one to finesse that subtle issue.
	www.nap.edu /openbook.php?record_id=2026&page=109 (6308 words)

	News \| TimesDaily.com \| TimesDaily \| Florence, Alabama (AL)
		A planar straight line graph is a graph in which the vertices are embedded as points in the Euclidean plane, and the edges are embedded as non-crossing line segments.
		A Euclidean graph is a graph in which the vertices represent points in the plane, and the edges are assigned lengths equal to the Euclidean distance between those points.
		The Euclidean minimum spanning tree is the minimum spanning tree of a Euclidean complete graph.
	www.timesdaily.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Geometric_graph_theory (743 words)

	Problem 5: Euclidean Minimum Spanning Tree
		But in the geometric setting, the graph is complete, so a time bound linear in the number of edges, m, is quadratic in the number of points, n.
		Euclidean minimum spanning trees and bichromatic closest pairs.
		A minimum spanning tree algorithm with inverse-Ackermann type complexity.
	maven.smith.edu /~orourke/TOPP/P5.html (248 words)

	Delaunay triangulation - Education - Information - Educational Resources - Encyclopedia - Music
		Delaunay triangulations maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid "sliver" triangles.
		For a set P of points in the (n-dimensional) Euclidean space, the Delaunay triangulation is the triangulation DT(P) of P such that no point in P is inside the circum-hypersphere of any simplex in DT(P).
		The Euclidean minimum spanning tree of a set of points is a subset of the Delaunay triangulation of the same points, and this can be exploited to compute it efficiently.
	www.music.us /education/D/Delaunay-triangulation.htm (649 words)

	Euclidean Minimum Spanning Tree - meaning of word
		The Euclidean minimum spanning tree or EMST is a minimum spanning tree of a set of points in the plane (mathematics) (or more generally in
		First, there is a useful property about minimum spanning trees that we will use: if we have a cycle of points, such as ''v''
		== Applications == An obvious application of Euclidean minimum spanning trees is to find the cheapest network of wires or pipes to connect a set of places, assuming the links cost a fixed amount per unit length.
	www.wordsonline.org /Euclidean_minimum_spanning_tree (1090 words)

	Algorithms for Torsion Angle Selection
		A spanning tree is a set of edges in a graph for which there is a single path from every vertex to every other vertex.
		A minimum spanning tree on a weighted graph, selects the spanning tree with the smallest possible total edge weights (see Figure 4.3).
		Finding the minimum spanning tree sounds more difficult than it is. Kruskal's algorithm is a polynomial time algorithm for selecting a graph's minimum spanning tree.
	www.sju.edu /~sforman/thesis-html/node4.html (3320 words)

	Geometry in Action: Minimum Spanning Trees
		Pope use geometric minimum spanning trees to model locality of particle interactions in turbulent fluid flows.
		Minimal spanning tree analysis of fungal spore spatial patterns, C.
		Dan Lauer uses minimum spanning trees to understand the large-scale structure of the universe.
	www.ics.uci.edu /~eppstein/gina/mst.html (289 words)

	Minimum spanning tree - Definition, explanation
		, the exact expected size of the minimum spanning tree has been computed for small complete graphs.
		Otakar Boruvka on Minimum Spanning Tree Problem (translation of the both 1926 papers, comments, history) (2000) Jaroslav Nesetril, Eva Milková, Helena Nesetrilová (section 7 gives his algorithm, which looks like a cross between Prim's and Kruskal's)
		A Minimum Spanning Tree Algorithm with Inverse-Ackermann Type Complexity, Bernard Chazelle, 1999
	www.calsky.com /lexikon/en/txt/m/mi/minimum_spanning_tree.php (653 words)

	CAIDA : tools : visualization : walrus
		Because the specifics of the supplied spanning tree greatly affect the resulting display, it is crucial that the user supply a spanning tree that is both meaningful for the underlying data and appropriate for the desired insight.
		The prominence and orderliness that Walrus gives to the links in the spanning tree, in contrast to all other links, means that an arbitrarily chosen spanning tree may create a misleading or ineffective visualization.
		The spanning tree must be meaningful with respect to the problem domain, dataset, research hypothesis, or in some other way.
	www.caida.org /tools/visualization/walrus (1785 words)

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