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Width (other)
Width is a measure of distance from side to side, measuring across an object at right angles to the length. Width may also refer to: Graph theory * Width of a partial order - the cardinality of a maximum antichain. * Width of a tree decomposition of an undirected graph, one less than the size of the largest vertex-set in the decomposition. * Width of a path decomposition of an undirected graph, one less than the size of the largest set in the decomposition * Width of a branch decomposition of an undirected graph, the maximum number of shared vertices of any pair of subgraphs formed by removing an edge from the tree. * Clique-width In graph theory, the clique-width of a graph is a parameter that describes the structural complexity of the graph; it is closely related to treewidth, but unlike treewidth it can be small for dense graphs. It is defined as the minimum number of ... of a graph, the minimum number of distinct labels needed to construct ''G'' by operations that cre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Width
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system, the base unit for length is the metre. Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in. Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, width, breadth, and depth. ''Height'' is used when there is a base from which vertical measurements can be taken. ''Width'' and ''breadth'' usually refer to a shorter dimension than ''length''. ''Depth'' is used for the measure of a third dimension. Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squared) and volume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Width (partial Order)
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are incomparable. The size of the largest antichain in a partially ordered set is known as its width. By Dilworth's theorem, this also equals the minimum number of chains (totally ordered subsets) into which the set can be partitioned. Dually, the height of the partially ordered set (the length of its longest chain) equals by Mirsky's theorem the minimum number of antichains into which the set can be partitioned. The family of all antichains in a finite partially ordered set can be given join and meet operations, making them into a distributive lattice. For the partially ordered system of all subsets of a finite set, ordered by set inclusion, the antichains are called Sperner families and their lattice is a free distributive lattice, with a Dedekind number of elements. More generally, counting the number of antichains of a finite p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Treewidth
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests A forest is an ecosystem characterized by a dense community of trees. Hundreds of definitions of forest are used throughout the world, incorporating factors such as tree density, tree height, land use, legal standing, and ecological functio .... An example of graphs with treewidth at most 2 are the series–parallel graphs. The maximal graphs with treewidth exactly are called '' -trees'', and the graphs with treewidth at most are called '' partial -trees''. Many other well-studied graph families also have bounded treewidth. Treewidth may be formally defined in several equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal completi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pathwidth
In graph theory, a path decomposition of a graph is, informally, a representation of as a "thickened" path graph, and the pathwidth of is a number that measures how much the path was thickened to form . More formally, a path-decomposition is a sequence of subsets of vertices of such that the endpoints of each edge appear in one of the subsets and such that each vertex appears in a contiguous subsequence of the subsets,. and the pathwidth is one less than the size of the largest set in such a decomposition. Pathwidth is also known as interval thickness (one less than the maximum clique size in an interval supergraph of ), vertex separation number, or node searching number. Pathwidth and path-decompositions are closely analogous to treewidth and tree decompositions. They play a key role in the theory of graph minors: the families of graphs that are closed under graph minors and do not include all forests may be characterized as having bounded pathwidth, and the "vortices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branchwidth
In graph theory, a branch-decomposition of an undirected graph ''G'' is a hierarchical clustering of the edges of ''G'', represented by an unrooted binary tree ''T'' with the edges of ''G'' as its leaves. Removing any edge from ''T'' partitions the edges of ''G'' into two subgraphs, and the width of the decomposition is the maximum number of shared vertices of any pair of subgraphs formed in this way. The branchwidth of ''G'' is the minimum width of any branch-decomposition of ''G''. Branchwidth is closely related to tree decomposition, tree-width: for all graphs, both of these numbers are within a constant factor of each other, and both quantities may be characterized by forbidden graph characterization, forbidden minors. And as with treewidth, many graph optimization problems may be solved efficiently for graphs of small branchwidth. However, unlike treewidth, the branchwidth of planar graphs may be computed exactly, in polynomial time. Branch-decompositions and branchwidth may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique-width
In graph theory, the clique-width of a graph is a parameter that describes the structural complexity of the graph; it is closely related to treewidth, but unlike treewidth it can be small for dense graphs. It is defined as the minimum number of labels needed to construct by means of the following 4 operations : #Creation of a new vertex with label (denoted by ) #Disjoint union of two labeled graphs and (denoted by G \oplus H) #Joining by an edge every vertex labeled to every vertex labeled (denoted by ), where #Renaming label to label (denoted by ) Graphs of bounded clique-width include the cographs and distance-hereditary graphs. Although it is NP-hard to compute the clique-width when it is unbounded, and unknown whether it can be computed in polynomial time when it is bounded, efficient approximation algorithms for clique-width are known. Based on these algorithms and on Courcelle's theorem, many graph optimization problems that are NP-hard for arbitrary graphs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degeneracy (graph Theory)
In graph theory, a -degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree (graph theory), degree at most k. That is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of k for which it is k-degenerate. The degeneracy of a graph is a measure of how dense graph, sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph. Degeneracy is also known as the -core number, width, and linkage, and is essentially the same as the coloring number or Szekeres–Wilf number (named after ). The k-degenerate graphs have also been called -inductive graphs. The degeneracy of a graph may be computed in linear time by an algorithm that repeatedly removes minimum-degree vertices. The Connected component (graph theory), connected components that are left after all vertices of degree less than k have been (repeatedly) removed are called the - ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Bandwidth
In graph theory, the graph bandwidth problem is to label the vertices of a graph with distinct integers so that the quantity \max\ is minimized ( is the edge set of ). The problem may be visualized as placing the vertices of a graph at distinct integer points along the ''x''-axis so that the length of the longest edge is minimized. Such placement is called linear graph arrangement, linear graph layout or linear graph placement. The weighted graph bandwidth problem is a generalization wherein the edges are assigned weights and the cost function to be minimized is \max\. In terms of matrices, the (unweighted) graph bandwidth is the minimal bandwidth of a symmetric matrix which is an adjacency matrix of the graph. The bandwidth may also be defined as one less than the maximum clique size in a proper interval supergraph of the given graph, chosen to minimize its clique size . Cyclically interval graphs For fixed k define for every i the set I_k(i) := [i, i+k+1). G_k(n) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Width Of A Hypergraph
In graph theory, there are two related properties of a hypergraph that are called its "width". Given a hypergraph ''H'' = (''V'', ''E''), we say that a set ''K'' of edges ''pins'' another set ''F'' of edges if every edge in ''F'' intersects some edge in ''K''. Then: * The width of ''H'', denoted w(''H''), is the smallest size of a subset of ''E'' that pins ''E''. * The matching width of ''H'', denoted mw(''H''), is the maximum, over all matchings ''M'' in ''H'', of the minimum size of a subset of ''E'' that pins ''M''. Since ''E'' contains all matchings in ''E'', for all ''H'': w(''H'') ≥ mw(''H''). The width of a hypergraph is used in Hall-type theorems for hypergraphs. Examples Let ''H'' be the hypergraph with vertex set V = and edge set:''E'' = The widths of ''H'' are: * w(''H'') = 2, since ''E'' is pinned e.g. by the set , and cannot be pinned by any smaller set. * mw(''H'') = 1, since every matching can be pinned by a single edge. There are two matchings: is pinn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
%$WIDTH%
An environment variable is a user-definable value that can affect the way running processes will behave on a computer. Environment variables are part of the environment in which a process runs. For example, a running process can query the value of the TEMP environment variable to discover a suitable location to store temporary files, or the HOME or USERPROFILE variable to find the directory structure owned by the user running the process. They were introduced in their modern form in 1979 with Version 7 Unix, so are included in all Unix operating system flavors and variants from that point onward including Linux and macOS. From PC DOS 2.0 in 1982, all succeeding Microsoft operating systems, including Microsoft Windows, and OS/2 also have included them as a feature, although with somewhat different syntax, usage and standard variable names. Design In all Unix and Unix-like systems, as well as on Windows, each process has its own separate set of environment variables. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Per Ove Width
Per Ove Width (born 27 March 1939 in Tønsberg) is a Norwegian politician for the Progress Party. He was elected to the Norwegian Parliament from Vestfold in 1997, and has been re-elected on two occasions. He had previously served in the position of deputy representative during the terms 1989–1993 and 1993–1997. Width held various positions in Tjøme Tjøme () is a List of former municipalities of Norway, former municipality in Vestfold county, Norway. The island municipality existed from 1838 until its dissolution in 2018. The area is now part of Færder Municipality. The administrative ce ... municipality council from 1983 to 1995, serving as deputy mayor in the periods 1987–1991, 1993–1995 and 2003–2007. References * 1939 births Living people Progress Party (Norway) politicians Politicians from Tønsberg Members of the Storting 2001–2005 Members of the Storting 1997–2001 Members of the Storting 2005–2009 {{Norway-politician-1930s-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Width Of A Circle
"The Width of a Circle" is a song written by the English musician David Bowie in 1969 for his 1970 album, '' The Man Who Sold the World''. Recorded during the spring of 1970, it was released later that year in the United States and in April 1971 in the UK. The opening track on the album, it features hard rock and heavy metal overtones. Bowie had performed a shorter version of the song in concerts for several months before recording it. Featuring Mick Ronson's lead guitar work and occasional choral effects from the band, this 8-minute song is divided into two parts. The music takes on a heavy R&B quality in the second half, where the narrator enjoys a sexual encounter – with God, the Devil or some other supernatural being, according to different interpretations – in the depths of Hell.Martin Aston (2007). "Scary Monster", ''MOJO 60 Years of Bowie'': pp.24-25 Live versions Several live versions of the song have been released: *A 10-minute, 43-second version recorde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
