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# Topic: Hypergraph

###### In the News (Thu 19 Apr 18)

 Hypergraph - Wikipedia, the free encyclopedia Formally, an hypergraph is a pair (X,E) where X is a set of elements, called nodes or vertices, and a E is a set of subsets of X, called hyperedges. For instance, a hypergraph homomorphism is a map from the vertex set of one hypergraph to another such that each edge maps to one other edge. A hypergraph automorphism is an isomorphism from a vertex set into itself, that is a relabeling of vertices. en.wikipedia.org /wiki/Hypergraph   (424 words)

 PlanetMath: hypergraph   (Site not responding. Last check: 2007-11-07) A hypergraph is the same thing as a simple incidence structure, but with terminology that focuses on the relationship with graphs. This is version 11 of hypergraph, born on 2002-10-07, modified 2005-04-08. I hit on the idea of a hypergraph (from the perspective of generalising geometry, not from graph theory) a few months ago, and have been earnestly looking for any mention of what I called 'generalised polygons' (only I realised somebody else had got there first with that term). planetmath.org /encyclopedia/Hypergraph.html   (298 words)

 HyperGraph: Using Hypermedia to Teach Computer Graphics HyperGraph is being used as the primary text for computer graphics and related courses at Georgia State University (GSU). The HyperGraph project is a joint effort of the ACM SIGGRAPH Education Committee, the National Science Foundation, and involves faculty from multiple institutions and disciplines. HyperGraph is used both for lecture presentation and for self-paced individual student learning. www.cs.gsu.edu /mathcsc/research/papers/hypgraf.html   (2583 words)

 HG4TM - Hypergraph Topic Map To meet the requirements both of RM4TM and of hypergraph structure integrity, the subjects and the hypergraph are defined as distinct sets, and a representation mapping is defined between the two sets. The hypergraph is used to represent the structure of assertions. Note that "Subject Location Uniqueness" is not achieved in the hypergraph, since the same subject can be represented by two elements of the hypergraph, for example by a vertex in some place, and by an edge in another one (for an assertion). perso.wanadoo.fr /universimmedia/topicmaps/hypergraph/hg4tm.htm   (974 words)

 Hypergraph The corrector is placed near the bore of the main mirror and the system shows perfect performance on a 4" large field that is nearly diffraction limited. The spot size on the plane field of the Hypergraph is more than 20 times smaller compared to a conventional Schmidt-Cassegrain, about 10 times smaller compared to a classical Cassegrain and about 8 times smaller compared to a Ritchey-Chretien telescope. The visual performance is also marvelous, making the Hypergraph a perfect all-round telescope. www.astrooptik.com /Komplettgeraete/Hypergraph_E.htm   (334 words)

 Altair HyperGraph 7.0 HyperGraph provides design, test and engineering staffs with an intuitive plotting and data analysis package for efficient data analysis. HyperGraph's automatic plot builder generates a series of fully annotated XY plots, bar charts and complex plots directly from a data files. HyperGraph supports Linear, Log10, Log20 and Decibel axis scaling, a variety of line styles, symbols and colors, as well as full user-control of text size, color and style. www.altair.com /software/hw_hg.htm   (750 words)

 Vitaly Voloshin: Basic concepts on mixed hypergraph coloring   (Site not responding. Last check: 2007-11-07) of a mixed hypergraph is a mapping c: X → {1,2,...,k} such that: In a colorable mixed hypergraph H, the maximum (minimum) number of colors over all strict k-colorings is called the The number of proper k-colorings of a mixed hypergraph H is a polynomial in k; it is denoted spectrum.troy.edu /~voloshin/basic.html   (561 words)

 Project Hypergraph The purpose of the assignment is to implement a hypergraph. Such a methodology results in a hypergraph that is optimized for memory efficiency. A hypergraph is simply defined as a single list of elements, which can be any combination of graphs and/or nodes. www.iit.edu /~blasdar/cs495/blasdar/p2/doc/graph.html   (1294 words)

 HyperGraph Partitioning Algorithm (HGPA) The second algorithm is a direct approach to cluster ensembles that re-partitions the data using the given clusters as indications of strong bonds. The cluster ensemble problem is formulated as partitioning the hypergraph by cutting a minimal number of hyperedges. However, in standard hypergraph partitioning they have equivalent quality since both cut the same number of hyperedges. www.lans.ece.utexas.edu /~strehl/diss/node81.html   (267 words)

 Hypergraphs Extremal set theory is concerned with problems of the following type: determine (or estimate) the maximum number of edges of a hypergraph satisfying certain conditions. There are no triangles, i.e., there is no set of three edges that intersect pairwise but have an empty intersection. Note that the maximum possible number of edges in a 3-uniform hypergraph is people.cs.uchicago.edu /~laci/reu04/n05.hdir/node2.html   (237 words)

 Hypergraph   (Site not responding. Last check: 2007-11-07) If you change the default Hypergraph colors (Options > Customize UI > Colors), some objects may lack contrast or appear to be invisible. The IK Handle Tool behaves differently in the Hypergraph than it does in a model view. However, in the Hypergraph after you select the first joint you must hold down the Shift key to extend the selection for the end joint. www.c3.hu /docs/maya/ReleaseNotes/ReleaseNotesUI4.html   (241 words)

 hypergraph   (Site not responding. Last check: 2007-11-07) Formal Definition: A hypergraph G can be defined as a pair (V, E), where V is a set of vertices, and E is a set of hyperedges between the vertices. So G = (people, family) is a hypergraph. Contrast this with the binary relations "married to," which connects a man and a woman, or "child of," which is directed from a child to his or her father or mother. www.nist.gov /dads/HTML/hypergraph.html   (186 words)

 SAT Workshop, Siena The transversal hypergraph of H is the hypergraph Tr(H) = (V, F) such that F is the family of all minimal (w.r.t. A coterie C is, using hypergraph terminology, an intersecting hypergraph. It is known that nondominatedness coincides with the property that C is a self-transversal hypergraph, i.e., a hypergraph H is identical to its transversal hypergraph. www.ece.uc.edu /~franco/Sat-workshop/sat-workshop-open-problems.html   (1684 words)

 Association Rule Hypergraph Partitioning Algorithm   (Site not responding. Last check: 2007-11-07) These frequent item sets are then used to group items into hypergraph edges, and a hypergraph partitioning algorithm [KAKS97] is used to find the item clusters. A hypergraph is an extension of a graph in the sense that each hyperedge can connect more than two vertices. Next, a hypergraph partitioning algorithm is used to partition the hypergraph such that the weight of the hyperedges that are cut by the partitioning is minimized. maya.cs.depaul.edu /~mobasher/papers/wits/node3.html   (394 words)

 GSRC Calibrating Achievable Design Bookshelf: Hypergraph Formats This allows it to be used as a converter between the two, or simply to check compliance with the standard. If not, then after checking your file thoroughly send us email (it's of course possible that there's a bug in HGConv..the odds of this will dimish as more people use it). HGConv1.0 produces a number of useful statistics about the Hypergraph, including counts of edges, nodes, terminals and non-terminals, as well as a profile of node weights and widths and edge degrees. vlsicad.ucsd.edu /GSRC/bookshelf/Slots/Fundamental/HGraph/HGraph1.1.html   (1645 words)

 Improved Algorithms for Hypergraph Bipartitioning Multilevel Fiduccia-Mattheyses (MLFM) hypergraph partitioning \cite{AlpertHK97,KarypisAKS97,KarypisK99} is a fundamental optimization in VLSI CAD physical design. In this work, we present two sets of results: (i) new techniques for flat FM-based hypergraph partitioning (which is the core of multilevel implementations), and (ii) a new multilevel implementation that offers leading-edge performance. Our new techniques for flat partitioning confirm the conjecture from \cite{CaldwellKM99e}, suggesting that {\em specialized partitioning heuristics} may be able to {\em actively exploit} fixed nodes in partitioning instances arising in the driving top-down placement context. www.gigascale.org /pubs/54.html   (338 words)

 GSRC Calibrating Achievable Design Bookshelf: Netlist/Hypergraph Slot It can be viewed as a libary of node types in the hypergraph. Each vertex in the.nodes file is an instance of a master node (an identical copy). The format is similar to the.net and.netD formats, as it specifes nets by listing their incident nodes and optionally the pin on the node. vlsicad.ucsd.edu /GSRC/bookshelf/Slots/Fundamental/HGraph   (1260 words)

 [No title] The research is aimed at both the study of hypergraph properties [GLNP89,GLNP93,NPM94] and of optimization hypergraph problems such as shortest hyperpaths, minimum cuts and minimum cost hyperflows. In particular, a Simplex algorithm for the Minimum Cost Flow Problem on capacitated directed hypergraphs, based on the characterization of the basis structures in terms of spanning hypertrees, has been proposed [CGS92,CGS97,GLS96]. Furthermore, as it is pointed out in the Logical Inference and Optimization section, hypergraphs provide a powerful tool to model and solve a wide class of logical inference problems. www.di.unipi.it /di/groups/optimize/hygraph.html   (797 words)

 hypergraph - Board Index I suspect you are gettin a tad confused between hierachical relationships in a scene (DAG) diagram, and the flow of information in a dependency graph (DG) network. If you then decide to graph the up and/or down stream connections, the hypergraph is displaying node connection relationships in a more universal fashion, as a dependancy graph, information flowing left to right (or top to bottom). I think you may have had a few typos in your post, where you repeated your descripton of [makesnurbSphere] twice, i assume you just ment [nurbsSphere] for one, the transform node,...which i think you also ment as the first node in your 'diagram' of the up'n'down stream connections. www.highend3d.com /boards/index.php?showtopic=60210&b=1&st=&p=&   (932 words)

 Hypergraph - Hyperbolic graphs and trees : Home   (Site not responding. Last check: 2007-11-07) Hypergraph - Hyperbolic graphs and trees : Home HyperGraph is an open source project which provides java code to work with hyperbolic geometry and especially with hyperbolic trees. It provides a very extensible api to visualize hyperbolic geometry, to handle graphs and to layout hyperbolic trees. hypergraph.sourceforge.net   (107 words)

 Umit V Catalyurek -- Software PaToH (Partitioning Tools for Hypergraph) is a Multilevel Hypergraph Partitioning tool that I have developed during my PhD studies at Bilkent University (1994-1999). It was the fastest hypergraph partitioner when I wrote it, and probably it is still the fastest partitioner. Catalyurek and C. Aykanat, “A Fine-Grain Hypergraph Model for 2D Decomposition of Sparse Matrices,” in Proceedings of International Parallel and Distributed Processing Symposium (IPDPS), 8th International Workshop on Solving Irregularly structured Problems in Parallel (Irregular 2001), San Francisco, April 2001. bmi.osu.edu /~umit/software.html   (386 words)

 XSI Moving from Maya to XSI / Hypergraph vs. Schematic XSI Moving from Maya to XSI / Hypergraph vs. Schematic Flash 7 player is required to play the above content. In this lesson we will get acquainted with the Schematic and its similarities / dissimilarities with the Hypergraph. www.digitaltutors.com /digital_tutors/video_details.php?v=667   (126 words)

 Class graph.HyperGraph A hypergraph is a generalized graph in the sense that it is a hierarchical composition of smaller graphs (subgraphs). Any two nodes within the hypergraph can be linked together with an edge, even if the nodes exist in different subgraphs. Inserts a new edge at the specified address. www.iit.edu /~blasdar/graph/graph.HyperGraph.html   (1004 words)

 Vitaly Voloshin: Mixed Hypergraph Coloring: Contents   (Site not responding. Last check: 2007-11-07) Chapter 2 Mixed hypergraphs and the upper chromatic number 4.6 UC mixed hypergraphs with χ ≥ n-2 Chapter 11 Coloring block designs as mixed hypergraphs spectrum.troy.edu /~voloshin/contents.html   (58 words)

 HG4TM - Hypergraph Topic Map To meet RM4TM requirements A, C, T and R are disjoint from each other. is the set of subjects, H is the hypergraph representation of S. Red downward dotted arrows figure the "representation function" www.mondeca.com /hypergraph/hg4tm.htm   (990 words)

 CGTalk - renaming in outliner/hypergraph i may be an idiot, but is there any easier way to rename things when you have them selected than double clicking in the outliner or right clicking to "rename" in the hypergraph? Ctrl + double click in editors like Hypergraph and Hypershade To change painlessly a layer’s name select an object that’s in it and click on the layer’s name in the channel box. forums.cgsociety.org /showthread.php?t=295759   (366 words)

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