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Topic: Spanning tree

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Spanning tree (mathematics)

Spanning tree (networks)

Internet group management protocol

Local area network

Ethernet

IPTV

	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/SmallestSpanningTree.html (114 words)

	Transform - Spanning Tree (Site not responding. Last check: 2007-10-19)
		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.
		Although points sets will often have one and only one spanning tree arrangement that results in the lowest distance, regularly arranged point sets (such as those in orthogonal grids) can have many different spanning tree networks drawn that will all have the same, lowest, total length of links.
		The minimum spanning tree transform simply guarantees that no tree can be drawn that uses less material than the spanning tree it finds.
	www.manifold.net /doc/700/transform_spanning_tree.htm (451 words)

	Computation - Operations Research Models and Methods
		For the minimal or maximal spanning tree problems, each arc is assigned a length.
		The goal of the problem is to select a spanning tree so that the total of the lengths of the selected arcs is minimized or maximized.
		The variables describe the tree below, which is the minimal spanning tree rooted at node 1.
	www.me.utexas.edu /~jensen/ORMM/computation/unit/combin/tree_span.html (1262 words)

	Spanning tree protocol - Wikipedia, the free encyclopedia
		Spanning tree is based on an algorithm invented by Radia Perlman while working for Digital Equipment Corporation.
		Other switches in the network that use spanning tree will use the same algorithmic process to calculate the shortest path to the root bridge and so produce a loop free tree topology where multiple paths to the root bridge exist.
		Cisco's name for this is per VLAN spanning tree (PVST and PVST+ which is the default protocol used by Cisco switches).
	en.wikipedia.org /wiki/Spanning_tree_protocol (1135 words)

	Riverstone Networks - Spanning Tree: Death is Not an Option
		This article is an overview of the progression of both the spanning tree algorithm and recent modifications that have made it an important technology for today's metro networks.
		Spanning Tree is a protocol with a life story.
		It reduces the topology to a tree structure that guarantees complete connectivity (that's why it is a "spanning" tree).
	www.riverstonenet.com /solutions/spanning_tree.shtml (2617 words)

	Minimum Spanning Tree
		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.
		Algorithms for generating spanning trees in order from minimum to maximum weight are presented in [Gab77].
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE161.HTM (1238 words)

	[No title]
		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)

	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.
		Such a minimum spanning tree can be refined by inserting a Steiner point whenever the edges of the minimum spanning tree incident on a vertex form an angle of less than 120 degrees between them.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE181.HTM (1383 words)

	Greedy Algorithms
		spanning tree of a graph is any tree that includes every vertex in the graph.
		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.
		Spanning trees construct a sparse sub graph that tells a lot about the original graph.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/Greedy/mst.htm (834 words)

	Spanning tree (mathematics) - Wikipedia, the free encyclopedia
		In the mathematical field of graph theory, a spanning tree T of a connected, undirected graph G is a tree composed of all the vertices and some (or perhaps all) of the edges of G.
		If G is a multigraph and e is an edge of G, then the number t(G) of spanning trees of G satisfies the deletion-contraction recurrence t(G)=t(G-e)+t(G/e), where G-e is the multigraph obtained by deleting e and G/e is the contraction of G by e, where multiple edges arising from this contraction are not deleted.
		A spanning tree chosen randomly from among all the spanning trees with equal probability is called a uniform spanning tree (UST).
	en.wikipedia.org /wiki/Spanning_tree_(mathematics) (438 words)

	spanning tree protocol - EnterpriseNetworkingPlanet - News, trends and advice for network managers
		Using the spanning tree algorithm, STP provides path redundancy while preventing undesirable loops in a network that are created by multiple active paths between stations.
		To establish path redundancy, STP creates a tree that spans all of the switches in an extended network, forcing redundant paths into a standby, or blocked, state.
		Without spanning tree in place, it is possible that both connections may be simultaneously live, which could result in an endless loop of traffic on the LAN.
	networking.webopedia.com /TERM/S/spanning_tree_protocol.html (213 words)

	Configuring Spanning Tree (Site not responding. Last check: 2007-10-19)
		Spanning tree is a link management protocol that provides path redundancy while preventing undesirable loops in the network.
		Spanning tree defines a tree with a root switch and a loop-free path from the root to all switches in the extended Layer 2 network.
		Note If you disable spanning tree for a TrBRF using the set spantree disable command, the logical ports of the TrBRF are placed in the forwarding state regardless of the state you configured using the set spantree portstate command.
	www.cisco.com /univercd/cc/td/doc/product/lan/cat5000/rel_5_2/config/spantree.htm (4569 words)

	Minimal Spanning Trees
		A spanning tree is a tree that includes all of the nodes in a graph.
		Finally, for our purposes, a minimal spanning tree is the spanning tree the sum of whose edge weights is less than or equal to the sum of the weights of any other spanning tree for this graph.
		Notice, by the way that, for physical travel, trees are not the solution since they not consider the distance to return from any dead end branch of the tree.
	www.delphiforfun.org /Programs/Math_Topics/MinimalSpanningTrees.htm (1086 words)

	Spanning Tree Relaxation (Site not responding. Last check: 2007-10-19)
		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 (114 words)

	LAN - Spanning Tree
		The spanning tree algorithm was developed for networks needing more than one bridge to connect their networks and to do so in a fashion that prevents loops.
		Spanning tree's purpose is to automate the process of calculating loop free paths through the physical networks to each LAN.
		The Spanning Tree Algorithm is designed to provide a loop free path from any given switch to the root bridge.
	www.inetdaemon.com /tutorials/lan/bridging/spanning_tree.shtml (304 words)

	Spanning Tree (Site not responding. Last check: 2007-10-19)
		Defn: A spanning tree is a subgraph T of a CFG g that is a tree rooted at Entry that spans (contains) all the nodes in the CFG, and where all the edges in T are edges in the CFG.
		Tree edges: edges in both CFG and spanning tree 2.
		Advancing edges: X -> Y not tree edge, but where Y is a proper descendant of X in the spanning tree 3.
	www.cs.wm.edu /~noonan/cs652/spantree/slide1.html (111 words)

	Minimum spanning tree - Wikipedia, the free encyclopedia
		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.
	en.wikipedia.org /wiki/Minimum_spanning_tree (996 words)

	Lecture 17 - minimum spanning trees
		A spanning tree is a subgraph of G which has the same set of vertices of G and is a tree.
		A minimum spanning tree of a weighted graph G is the spanning tree of G whose edges sum to minimum weight.
		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.
	www.cs.sunysb.edu /~algorith/lectures-good/node17.html (1379 words)

	Networking 101: Understanding Spanning Tree
		Spanning tree will block one or more of the links until the active one becomes unusable, and then fail over to the other available link.
		Spanning Tree provides a means to control loops in such a way that you can have an Ethernet network that will "fail over" in the case of failed links.
		The root bridge in a spanning tree is the logical center, and sees all traffic on a network; don't rely on the election to choose which bridge becomes the root.
	www.enterprisenetworkingplanet.com /netsp/article.php/3580966 (1575 words)

	Minimum spanning trees
		On the other hand, if you draw a path tracing around the minimum spanning tree, you trace each edge twice and visit all points, so the TSP weight is less than twice the MST weight.
		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 (1692 words)

	Undirected Graphs and Minimum Spanning Trees
		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.
		Therefore T1, T2 and e form a minimum spanning subtree which must be part of a minimum spanning tree of G. The invariant really is invariant.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph/Undirected (1303 words)

	minimum spanning tree (Site not responding. Last check: 2007-10-19)
		Definition: A minimum-weight tree in a weighted graph which contains all of the graph's vertices.
		Note: A minimum spanning tree can be used to quickly find a near-optimal solution to the traveling salesman problem.
		The term "shortest spanning tree" may be more common in the field of operations research.
	www.nist.gov /dads/HTML/minimumSpanningTree.html (160 words)

	A Fast, Parallel Spanning Tree Algorithm for Symmetric Multiprocessors (SMPs)
		Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but often have no known efficient parallel implementations.
		A new and practical spanning tree algorithm for symmetric multiprocessors that exhibits parallel speedups on graphs with regular and irregular topologies; and
		An experimental study of parallel spanning tree algorithms that reveals the superior performance of our new approach compared with the previous algorithms.
	www-static.cc.gatech.edu /~bader/papers/SpanningTree.html (240 words)

	Intel® Express Gigabit Switch - Configuring Spanning Tree
		The Spanning Tree algorithm creates a single path through the network by making sure that if more than one path exists between two parts of a network, only one of those paths is used.
		Multilayer Spanning Trees are also isolated from the main legacy Spanning Tree, and are therefore smaller and converge faster.
		This is a huge advantage in a large switched network where a Spanning Tree reconfiguration could literally bring down the network for hours.
	www.intel.com /support/express/switches/1gb/sb/cs-011017.htm (888 words)

	Spanning Tree Protocol
		One risk of using the Spanning Tree Protocol is that the single route between two rings that are physically close together might not be the most direct path between those rings.
		The Spanning Tree Protocol uses a hierarchical control structure to determine which bridge interfaces are allowed to forward single-route explorer frames.
		Using the Spanning Tree Protocol ensures that there is only a single data path between any two end stations and eliminates data loops, as shown in Figure 2.
	www.novell.com /documentation/nias41/srbrgenu/data/hia0ypjo.html (1613 words)

	Intel® Express 10 Switch - Spanning Tree Basics
		Within the Spanning Tree Algorithm, switches connected in a LAN must detect potential "bridge loops", and then remove these loops by blocking the appropriate ports to other switches.
		However, by using the Spanning Tree Algorithm, Switch B breaks the loop and blocks its path to segment 3.
		If the network is extended by adding Switch D, the Spanning Tree Algorithm must be capable of adapting automatically to the new topology, that is Switch B stops looping by blocking the path to segment 3.
	www.intel.com /support/express/switches/10/sb/cs-014350.htm (887 words)

	O'Reilly Network -- Understanding Spanning Tree Protocol -- the Fundamental Bridging Algorithm (Site not responding. Last check: 2007-10-19)
		The Spanning Tree Protocol (STP) algorithm provides the missing component the Sprocket network needs to implement a redundant network without the redundant traffic paths.
		Spanning tree root bridges in redundant fault-tolerant environments.
		Once a tree is built and the BPDU exchange has settled down, the network is said to be in a state of convergence.
	www.oreillynet.com /pub/a/network/2001/03/30/net_2nd_lang.html (1258 words)

	PlanetMath: spanning tree
		Below is an example of a spanning tree
		For any tree there is exactly one spanning tree: the tree itself.
		This is version 3 of spanning tree, born on 2002-02-25, modified 2004-03-26.
	planetmath.org /encyclopedia/SpanningTree.html (59 words)

	What is spanning tree protocol? - a definition from Whatis.com
		The spanning tree protocol prevents the condition known as a bridge loop.
		The spanning tree algorithm determines the network (which computer hosts are in which segment) and this data is exchanged using Bridge Protocol Data Units (BPDUs).
		The spanning tree protocol and algorithm were developed by a committe of the IEEE.
	searchnetworking.techtarget.com /sDefinition/0,,sid7_gci214602,00.html (813 words)

	Minimal Spanning Tree Algorithm
		The ith value in this vector is an observation number, indicating that this observation and the ith observation should be linked in the minimal span- ning tree.
		This starts on one end of a diameter and numbers the points in a certain order so that points close together in Euclidean space tend to be close in the sequence.
		The second column presents the radial ordering, based on dis- tance from the center of the minimal spanning tree.
	www-stat.stanford.edu /~susan/courses/b494/index/node90.html (193 words)

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