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Sparse Topologies with Small Spectrum Size - Elsässer, Kralovic, Monien (2003) (Correct)
....of the most important algebraic invariants of a graph. Although in general a graph is not characterized uniquely by its spectrum, there is a strong connection between its eigenvalues and several structural properties of the graph such as the diameter, bisection width, isoperimetric number etc. See [5] for a selection of results in this area. This work was partially supported by the German Research Association (DFG) within the SFB 376 Massive Parallelit at: Algorithmen, Entwurfsmethoden, Anwendungen and by the IST Programme of the EU under contract number IST1999 14186 (ALCOM FT) The ....
Chung, F.R.K.: Spectral Graph Theory, American Mathematical Society, 1994
Global Connectivity and Expansion: long cycles and.. - Brandt, Broersma.. (2002) (Correct)
.... An obvious equivalent way to view f connectedness is as an expansion property, i.e. in terms of an isoperimetric inequality (such as (1) below) Isoperimetric inequalities have been investigated mainly for specific classes of graphs (such as higher dimensional grids and cubes; see e.g. 6] and [9] for references) while the focus in the study of expanders has largely been to construct (sparse) expanders with certain desired properties [9, 15] Our aim here di#ers from both these: rather than trying to determine for which f some specific graphs are f connected, or to construct f connected ....
.... Isoperimetric inequalities have been investigated mainly for specific classes of graphs (such as higher dimensional grids and cubes; see e.g. 6] and [9] for references) while the focus in the study of expanders has largely been to construct (sparse) expanders with certain desired properties [9, 15]. Our aim here di#ers from both these: rather than trying to determine for which f some specific graphs are f connected, or to construct f connected graphs for certain specific f,weshall think of f as given but arbitrary, and then try to relate the corresponding property of f connectedness to ....
F.R.K. Chung, Spectral Graph Theory , American Mathematical Society 1997.
Graph Laplacians, Nodal Domains, and Hyperplane.. - Biyikoglu.. (2002) (Correct)
....classes of graphs and for obtaining bounds on properties such as the diameter, girth, chromatic number, connectivity, etc. 4, 13, 14, 34, 36] More recently, the interest has shifted somewhat from the adjacency spectrum to the spectrum of the closely related graph Laplacian, see e.g. [12, 38, 49, 50]. Again, the dominating part of the theory is concerned with the eigenvalues. The eigenvectors of graphs, however, have received only sporadic attention on their own. Even the recent book on Eigenspaces of Graphs [15] contains only a few pages on the geometric properties of the eigenvectors which ....
F. R. K. Chung. Spectral Graph Theory, volume 92 of CBMS. American Mathematical Society, 1997.
Recognizing more unsatisfiable random k-SAT instances.. - Friedman, Goerdt.. (2001) (1 citation) (Correct)
....EX) EX= n EX) 1=n Therefore we get that with high probability X n (m=n) o(m) ut 1.2 Spectral considerations Eigenvalues of matrices associated with general graphs are somewhat less common at least in Computer Science applications than those of regular graphs. The monograph [Ch97] is a standard reference for the general case. The easier regular 6 case is dealt with in [AlSp92] The necessary Linear Algebra details cannot all be given here. They are very well presented in the textbook [St88] Let G = V; E) be an undirected graph (loopless and without multiple edges) ....
....eigenvalue bounds with high probability. These eigenvalue bounds certify that the graphs GF and HF do not have independent sets as required by Theorem 8 in order to be satis able. Again background from spectral graph theory can be found for regular graphs in [AlSp92] and for the general case in [Ch97] The linear algebra required is well presented in [St88] Let G = V; E) be a standard undirected graph and AG the adjacency matrix of G. Let AG s eigenvalues be ordered 1 n , with n = jV j. We say that G is separated if j i j 1 for i 1. With = max j i j this reads ....
Fan R. K. Chung. Spectral Graph Theory. American Mathematical Society, 1997.
Web Document Clustering Using Hyperlink Structures - He, Zha, Ding, Simon (2001) (1 citation) (Correct)
....PA 16802, fxhe,zhag cse.psu.edu. This work was supported in part by NSF grant CCR 9901986. NERSC Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, fxfhe,chqding,hdsimong lbl.gov. Supported by Department of Energy through an LBL LDRD fund. problems [7, 8]. This method was proposed by Shi and Malik and has been successfully used in image segmentation [28] It is well known that clustering web documents based entirely on the textual contents of the documents is not very effective in finding distinct topics [29] In the context of clustering web ....
F.R.K. Chung. Spectral Graph Theory. American Mathematical Society, 1997.
Linear Structures for Concurrency in Probabilistic.. - Di Pierro, Wiklicky (2001) (Correct)
....special simpli ed form of linear operators. On an operational level it is quite obvious how matrices can be utilised to encode transition graphs [8] The extension of this algebraic approach to in nite graphs, resulting in Hilbert space operators, is also well established (see e.g. 50] or [11]) One main contribution of our approach is to use these results to re formulate a transition system based semantics for probabilistic 28 concurrent languages as a denotational (i.e. compositional and xpoint) one. The linear semantics approach relates the semantics of quantitative languages to ....
Chung, F. R., \Spectral Graph Theory," Regional Conference Series in Mathematics 92, American Mathematical Society, Providence, Rhode Island, 1997.
A Unifying Theorem for Spectral Embedding and Clustering - Brand, Huang (2003) (6 citations) (Correct)
....the dot product of samples in an unknown feature space1 ; and locally linear embed ding (LEE) 23] uses a matrix containing correlations of samples barycentric coordinates. Spectral methods have been even more successful for data clusterings and graph partitionings: Spectral bipartitioning [9, 6] cuts a graph in two by thresholding the second eigenvector of the graph s normalized Laplacian matrix, and numerous clustering algorithms use selected eigenvectors of dot product or kernel matrices to re represent the data for clustering by simpler heuristics such as thresholding or Kmeans [25, ....
.... of PCA is well understood, virtually all other spectral inethods are motivated by imperfect analogies between data derived graphs and physical problems (e.g. harmonic analysis 2 and random walks3) or as approximations to other problems (e.g. vector quantization [2] min cut [27] or max flow [6]) Underlying all this work is the notion that the truncated eigenvector basis somehow makes the problem simpler for the subsequent analysis. Our theoretical goal is to explain how and why this works. Embeddings and clusterings imply loss of information, but there has been little effort to bound ....
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F.R. Chung. Spectral graph theory, volume 92 of CBMS Regional Conf.erence Series in Mathematics. American Mathematical Society, 1997.
Watermarking 2D Vector Maps in the Mesh-Spectral Domain - Ryutarou Ohbuchi Hiroo (2003) (Correct)
....Cayre et al. [5] applied the technique for watermarking 3D polygonal meshes in the frequency or mesh spectral domain. We borrow the technique for watermarking 2D vector digital maps by converting the maps into 2D meshes prior to watermarking. There are several different mesh Laplacian matrices [4, 3, 8]. We employ Biggs definition of mesh Laplacian R for the algorithm described in this paper. R (1) In the formula, I is the identity matrix and H is a diagonal matrix whose diagonal element H = 1 d is the reciprocal of the degree (or valence) of the vertexj. A is the adjacency matrix whose ....
F. R. K. Chung, Spectral Graph Theory, Number. 92 in Regional Conference Series in Mathematics, American Mathematical Society, 1997.
Approximation Hardness of Minimum Edge Dominating Set and.. - Chlebik, Chlebikova Self-citation (Mathematics) (Correct)
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F. R. K. Chung: Spectral Graph Theory, CBMS Regional Conference Series in Mathematics, American Mathematical Society, 1997, ISBN 0-8218-0315-8.
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F. Chung. Spectral Graph Theory. No. 92 in CBMS Regional Conference Series in Mathematics, American Mathematical Society, 1997.
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F. R. Chung. Spectral graph theory, volume 92 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, 1997.
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F. R. Chung. Spectral graph theory, volume 92 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, 1997.
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Fan R.K. Chung. Spectral graph theory, volume 92 of CBMS Regional Conference Series in Mathematics. American Mathematical Society, 1997.
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