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Topic: Connected components

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	Connected space - Wikipedia, the free encyclopedia
		The components form a partition of the space (that is, they are disjoint and their union is the whole space).
		The connected components of a space are disjoint unions of the path-connected components.
		The closure of a connected subset is connected.
	en.wikipedia.org /wiki/Connected_space (832 words)

	Connectedness - Wikipedia, the free encyclopedia
		For example, a path connected topological space is simply connected if each loop (path from a point to itself) in it is contractible; that is, intuitively, if there is essentially only one way to get from any point to any other point.
		For example, in graph theory, a connected graph is one from which we must remove at least one vertex to create a disconnected graph.
		The connectivity of a graph is the minimum number of vertices that must be removed, to disconnect it.
	en.wikipedia.org /wiki/Connectedness (765 words)

	PlanetMath: connected graph
		A connected graph is a graph such that there exists a path between all pairs of vertices.
		A connected component is a maximal (under inclusion) subset of vertices of any graph and any edges between them that forms a connected graph.
		This is version 4 of connected graph, born on 2002-03-02, modified 2005-08-09.
	planetmath.org /encyclopedia/ConnectedGraph.html (398 words)

	Image Analysis - Connected Components Labeling
		Connected component labeling works on binary or graylevel images and different measures of connectivity are possible.
		The connected components labeling operator scans the image by moving along a row until it comes to a point p (where p denotes the pixel to be labeled at any stage in the scanning process) for which V={1}.
		The two last examples showed that the connected component labeling is the easy part of the automated analysis process, whereas the major task is to obtain a good binary image which separates the objects from the background.
	homepages.inf.ed.ac.uk /rbf/HIPR2/label.htm (1485 words)

	Modeling a Connected Components Algorithm
		It is known that as edges are added randomly to a graph, the components in the graph grow slowly until a critical point, at which the entire graph begins to collapse into a single, large connected component.
		Connected components is an important problem underlying emerging areas of computational physics, as well as many areas of computer science.
		Above the transition boundary, one large component dominates the graph, and speedup is limited by remote memory contention and load imbalance; a minor modification alleviated the load imbalance problem, but a second, uncompleted change is required to eliminate the contention and to obtain good speedups for the connected phase.
	www.chg.ru /SC95PROC/465_SLUM/SC95.HTM (6404 words)

	Class Connection in theory Component-Assemblies (Site not responding. Last check: 2007-10-19)
		That means that whereever the connected-components relation holds between two components, there exists a connection component.
		This is logical existence; this connection object may not be present in the memory of a representation system.
		However, that object may not be unique, and the same connection object may be associated with several pairs of connected components.
	www-ksl.stanford.edu /pub/knowledge-sharing/ontologies/html/component-assemblies/CONNECTION.html (215 words)

	Connected and Path Connected
		Connected and path connected are not equivalent, as shown by the curve sin(1/x) on (0,1] union the origin.
		This is a connected half open interval, and its image under the continuous function f is connected.
		If c is connected, or path connected, it is an open set relative to itself, and it automatically meets the definition of locally connected, or locally path connected.
	www.mathreference.com /top,connect.html (1658 words)

	CONNECT - Find 3D Connected Components (WRF) (Site not responding. Last check: 2007-10-19)
		Connected components NX NY NZ connectivity #voxels #runs #components #comps_written: For each component: #runs, vol, area, (x, y, zl, zl)+ 512 544 544 6 76073721 2615676 534723 163110 6027 47382 37206 161 197 178 178 162 197 177 179....
		When two runs that were not known to be in the same component are determined to be adjacent, which means that two components are being unified, then the area of the combined component is the sum of the areas of the two original components, minus twice the overlap area.
		Components whose volume is one, or whose volume is greater than 100K are not considered interesting.
	www.ecse.rpi.edu /Homepages/wrf/Research/connect (2801 words)

	Segmentation-based clustering
		For components that consist of touching characters, we assume that prototypes resembling the characters which they contain are present and that we need to identify them and locate their positions.
		After the original segmentation (connected component analysis) and clustering, further segmentation is performed by specifying a threshold on the partial matches to the components.
		The same methodology is used as in the matching of partial components to prototypes except that the cost factor associated with a cut is replaced by one that is associated with component combination.
	www.cfar.umd.edu /~kia/Publications/Thesis/node3.html (2482 words)

	Connected Components (Site not responding. Last check: 2007-10-19)
		Discussion: The connected components of a graph represent, in grossest terms, the pieces of the graph.
		Connectivity is an essential invariant for network design and other structural problems.
		The first linear-time algorithm for strongly connected components is due to Tarjan [Tar72], with expositions including [Baa88, Eve79a, Man89].
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE159.HTM (1115 words)

	[No title]
		For example, in \figref{conn1}, 8-connectivity causes points in the exterior to be connected to points in the interior by the connected path shown.
		The connected components labeling operator scans the image by moving along a row until it comes to a point \em{p} (where \em{p} denotes the pixel to be labeled at any stage in the scanning process) for which \em{V={1}}.
		They make sure that two nearby components always have distinct colours by taking into account the colours of the neighbours of the component which is going to be assigned a colour.
	www.cee.hw.ac.uk /hipr/src/label.hpr (1592 words)

	Connected components of IP arc core (AB) (Site not responding. Last check: 2007-10-19)
		In addition to giant component, which is a genuine representative of the Internet core, the procedure of stripping retains in the data a number of smaller components.
		The dots on the diagonal are terminal components, i.e.
		A few of the largest connected components are given in the table below.
	www.caida.org /~broido/dest/conncp.html (380 words)

	Boost Graph Library: Connected Components (Site not responding. Last check: 2007-10-19)
		A connected component of an undirected graph is a set of vertices that are all reachable from each other.
		The total number of components is the return value of the function.
		The algorithm then records which component each vertex in the graph belongs to by recording the component number in the component property map.
	www.boost.org /libs/graph/doc/connected_components.html (326 words)

	IBM Visualization Data Explorer Bonuspak (Site not responding. Last check: 2007-10-19)
		This identifies which connected component each element lies in; all elements of one connected component will have the same "connected component" value, although the value itself will be arbitrary.
		Connected will not work correctly on Composite Fields in that no matching of connected components is made across partition boundaries.
		The "connected component" component is then moved into the data component and then the result is AutoColored and rendered.
	www.research.ibm.com /dx/bonuspak/html/bonuspak322.html (176 words)

	Bi-connected Components in the Journal Citation Report of the Social Science Citation Index
		A network component is called bi-connected if for every triple of vertices a, v, and w there exists a chain between v and w which does not include the vertex a.
		While a bi-connected network component provides us with a robust definition of a cluster, a factor or a principal component can be expected to remain very sensitive to the inclusion or exclusion of variables in the domain from which it is algorithmically extracted.
		At each round the largest component (rightmost column) is further decomposed after increasing the threshold level of the Pearson correlation with another 0.1 (leftmost column).
	users.fmg.uva.nl /lleydesdorff/sosci01/art (5613 words)

	[No title]
		In a digraph we define a strongly connected component to be a subgraph in which for any two vertices v,w there is a path from v to w and a path from w to v.
		Strong connectivity is an equivalence relation on the vertices of G. If G has only one strongly connected component, then G is said to be strongly connected.
		This shows that we can find the strongly connected components of G by keeping track of the roots of the components in the order they are (last) found.
	www.ececs.uc.edu /~cpurdy/lec25.html (737 words)

	Relation Connected-Components in theory Component-Assemblies (Site not responding. Last check: 2007-10-19)
		If (connected-components A B), then A and B must be components and neither can be a subcomponent-of of the other.
		Even in the case of a connection between physical components, the connection can represent abstract properties of the interaction of the two components.
		Note that the connection relation between connected components does not associate a name or type with the connection.
	www-ksl.stanford.edu /pub/knowledge-sharing/ontologies/html/component-assemblies/CONNECTED-COMPONENTS.html (150 words)

	SDMetrics User Manual - Connected Components (Site not responding. Last check: 2007-10-19)
		procedure is used to count the connected components in a graph.
		The default value is "false" and the procedure calculates the strongly connected components of the directed graph.
		When set to "true", the connected components of the underlying undirected graph will be computed (i.e., the direction of edges is ignored, an edge can always be followed in both ways).
	www.sdmetrics.com /manual/ConnComp.html (261 words)

	Strong connectivity
		If we can find all the strongly connected components of a graph, it would be easy to test whether any two vertices are strongly connected: just see if they're in the same component.
		The key property, that relates DFS to strong connectivity, is that strongly connected components form subtrees of the DFS tree.
		Since the components of the graph are just subtrees of the DFS tree, to find components, we just have to break tree at certain edges, and the components will be formed by what's left of the tree.
	www.ics.uci.edu /~eppstein/161/960220.html (2041 words)

	DACIA Architecture
		Components are connected through directed links, indicating the direction of the data flow within the application.
		An output port of a PROC is connected to an input port of another PROC.
		Sharing physical connections reduces the cost of establishing network connections in a highly dynamic application, where PROCs often connect to each other or they are disconnected.
	www.eecs.umich.edu /~aprakash/dacia/architecture.html (914 words)

	Boost Graph Library: Incremental Connected Components (Site not responding. Last check: 2007-10-19)
		This section describes a family of functions and classes that work together to calculate the connected components of an undirected graph.
		Maintain the connected components of a graph while adding edges using the disjoint-sets data structure.
		This function calculates the connected components of the graph, embedding the results in the disjoint-sets data structure.
	www.boost.org /libs/graph/doc/incremental_components.html (421 words)

	Strongly Connected Components
		This decomposition is important as it is used to divide a single directed graph into pieces for further processing.
		Output the vertices of each tree in the depth-first forest of step 3 as a separate strongly connected component.
		V is in a strongly connected component that consists of al v
	www.cs.fsu.edu /~cop4531/slideshow/chapter23/23-5.html (175 words)

	Connected Components (Site not responding. Last check: 2007-10-19)
		One of the most commonly used graph problems is that of finding the connected components of an undirected graph.
		Finding connected components is used in many diverse fields such as computer vision [1,
		In our work we are interested in the pragmatic aspects of parallel algorithms for finding connected components.
	www.cs.cmu.edu /~scandal/alg/connectivity.html (278 words)

	Strongly Connected Components, CS 410 Opt
		This chapter outlines an algorithm by Robert Tarjan, ref [1], that identifies all strongly connected components in a directed graph G with entry point e.
		Strongly connected components (SCC) are those subgrahs of G in which every node can be reach from every node in the SCC.
		A loop is a strongly connected component with additional restrictions.
	www.cs.pdx.edu /~herb/cs410f99/scc.htm (666 words)

	Connected-Components Algorithms For Mesh-Connected Parallel Computers - Kumar, Goddard, Prins (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		We present efficient parallel algorithms for finding the connected components of sparse and dense graphs using a mesh-connected parallel computer.
		Next, a representation of the adjacency matrix for a sparse graph with m edges is chosen that preserves the communication structure of the algorithm but...
		27 New connectivity and msf algorithms for ultracomputer and pr..
	citeseer.ist.psu.edu /kumar95connectedcomponents.html (572 words)

	Maintenance of 2- and 3-Edge-Connected Components of Graphs II
		Data structures and algorithms are presented to efficiently maintain the 2- and 3-edge-connected components of a general graph, under insertions of edges and nodes in the graph.
		Furthermore, a linear-time algorithm is presented for maintaining the 2-edge-connected components in case the initial graph is connected.
		Finally, a new solution is presented for the 2-vertex-connected components of a graph.
	epubs.siam.org /sam-bin/dbq/article/25777 (174 words)

	Control system - Wikipedia, the free encyclopedia
		A control system is a device or set of devices that manage the behavior of other devices.
		A control system is an interconnection of components connected or related in such a manner as to command, direct, or regulate itself or another system.
		There are two common types of controllers, with many variations and combinations: logic controls, and feedback or linear controls.
	en.wikipedia.org /wiki/Control_system (1300 words)

	Delta-Connected Components
		A connected component in the image is a maximal collection of uniformly colored pixels such that a path exists between any pair of pixels in the component.
		It is interesting to note that, in the previous paragraph, we defined connected components as a maximal collection of uniform color pixels such that a path existed between any pair of pixels.
		This algorithm is identical in analysis and complexity to the conventional connected components algorithm, as we are merely changing the criterion for checking the equivalence of two pixels.
	www.umiacs.umd.edu /research/EXPAR/papers/3449/node9.html (337 words)

	2.1. URL Syntactic Components (Site not responding. Last check: 2007-10-19)
		Some schemes use reserved characters like "?" and ";" to indicate special components, while others just consider them to be part of the path.
		However, there is enough uniformity in the use of URLs to allow a parser to resolve relative URLs based upon a single, generic-RL syntax.
		These components are defined as follows (a complete BNF is provided in Section 2.2):
	www.freesoft.org /CIE/RFC/1808/3.htm (222 words)

	Publications of the SPACES team
		Computing at least one point in each connected component of a real algebraic set is a basic subroutine to decide emptiness of semi-algbraic sets, which is a fundamental algorithmic problem in effective real algebraic geometry.
		More precisely, from a partition of the parameters' space, such that in any connected component of this partition the number of triple roots is constant, we need to compute one sample point by cell, in order to have a full description, in terms of cuspidality, of the different possible configurations.
		It was shown in a previous work that this ability to change posture without meeting a singularity is equivalent to the existence of a point in the workspace, such that a polynomial of degree four depending on the parameters of the manipulator and on the cartesian coordinates of the effector has a triple root.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

	Challenge Problems: Independent Sets in Graphs
		The smaller components are easily (within a few hours each) handled by either his Lovasz theta-based branch and bound code or by MINTO on the integer programming formulation, but the two largest components haven't cracked yet.
		The maximal independent sets for each component were shown to be optimal by formulating an integer program and then solving it with the help of the "MINTO" [MINTO] integer programming code.
		The smaller components were all handled by integer programming (or by his SDP-based branch and bound code), but the two largest components have not cracked yet.
	www.research.att.com /~njas/doc/graphs.html (2953 words)

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