spielman spectral graph theory 2018

Dan Spielman, Yale University Fall 2015. These are notes from a lecture given in another class that covered spectral graph theory. You are responsible for that (2016) Spectral graph sparsification in nearly-linear time leveraging efficient spectral perturbation analysis. Available here. The obvious prerequisites for this course are knowledge of linear Lecture 6-7: Spectral graph theory, spectral clustering, and community detection. We use support theory, in particular the fretsaw extensions of Shklarski and Toledo, to design preconditioners for the stiffness matrices of 2-dimensional truss structures that are stiffly connected. Expander graphs and some of their applications. Local Graph Clustering. Overview. You could think of this as a course in "Advanced Linear Algebra MAT 280 Harmonic Analysis on Graphs & Networks Reference Page (Fall 2019) The general introductory references; For general introduction to graphs and networks and significant applications: S. Fortunato, Community detection in graphs. Derive spectral clustering formulation as a relaxation of modularity maximization. Spectral Graph Theory Lecture 15 Tutte’s Theorem: How to draw a graph Daniel A. Spielman October 22, 2018 15.1 Overview We prove Tutte’s theorem [Tut63], which shows how to use spring embeddings to obtain planar drawings of 3-connected planar graphs. /Length 2825 %PDF-1.5 Community Detection. In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. Related Jupyter notebooks will appear on this page later. Spectral and Electrical Graph Theory (given at the Caesarea Rothschild Institute, Haifa, May 17, 2011. I find that almost every research question I address somehow relates 16 [Spielman], Ch. 3-4 whiteboard, scribe notes Sep 10 Cayley graphs Trevisan, Ch. Background required: Linear Algebra, Graph Theory, Probability. cayley graphs, strongly regular graphs and random graphs. Lap Chi Lau, University of Waterloo Fall 2015. Course notes from Stanford Winter 2011/2013. [Chau2015] Lap Chi Chau. NSF CCF-0634957: \Collaborative Research: Spectral Graph Theory and Its Applica- In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix. Tutte's theorem on drawing planar graphs using Spring networks. Most lectures will cover some essential element of Linear Algebra or NSF CCF-0915487: \Spectral Graph Theory, Point Clouds, and Linear Equation Solvers\. material. Cheeger's inequality: probably at least two different proofs of My Fall 2016 course on algorithmic spectral graph theory. Spectral Sparsification of Graphs (as given at the Weizmann Institute on May 15, 2011). The adjacency matrix of a simple graph is a real symmetric matrix and is therefore orthogonally diagonalizable; its eigenvalues are real algebraic integers. Community detection using ratio cut criterion. Spectral Sparsification of Graphs: Theory and Algorithms (with J. Batson, D. Spielman, and S-H. Teng), Communications of the ACM 2013. and [technical perspective] by Assaf Naor. Dan Spielman's course on spectral graph theory. Dan Spielman's Example Computations. We ask how well a given graph can be approximated by a … The book for the course is on this webpage. Within algorithmic spectral graph theory, both older structural results and recent algorithmic results will be presented. Properties of graph Laplacian. I will sometimes make use of concepts that every graduate student in Fall 2018. Readings: Ch. (1 ±) spectral sparsiﬁers of graph Laplacians with high probability. * Optimization problems on graph, such as maximum-flow, using continuous methods In the remaining part of the course, the students will read and present research papers related to the above topics. 3 0 obj %�� (Watson Center is 60 Sachem St, NOT AKW) You can find the schedule of lectures, lecture notes, and assignments, here. Topics to be covered in- ��P�&7`֩y Instructor: Dan Spielman. (with A. Marcus and D. Spielman), Proc. Luca Trevisan, UC Berkeley and Bocconi University Spring 2016. ICM 2014. May 8th, 2014, 3:30pm EEB 105 Dan Spielman, Department of Computer Science, Yale. U. Feige and R. Krauthgamer, Finding and certifying a large hidden clique in a semi-random graph. 2019 PDF 2018 Interlacing Families IV: Bipartite Ramanujan Graphs of All Sizes SIAM Journal on Computing, Vol 47, no. It is taught in the style of a math class, and will cover /Filter /FlateDecode and topology. One begins by selecting a … In this lecture, we will attempt to explain this success by proving, at least for planar graphs, that the second smallest Laplacian eigenvalue is small. Bounds on the Fiedler value of planar graphs. Grants NSF CCF-0915487: \Spectral Graph Theory, Point Clouds, and Linear Equation Solvers\. Connections to Spring and Electrical networks. Schur complements, effective resistance and some of their applications. Conversely, it doesn’t seem unreasonable that sheaves might have something to … groups, and elementary aspects of real analysis, complex analysis back to material covered in this course. Spectral Graph Theory, Fall 2015 Applied Mathematics 561/ Computer Science 662 . algebra and exposure to graph theory. Proceedings of the 53rd Annual Design Automation Conference on - DAC '16 , 1-6. Spectral and Algebraic Graph Theory Book in progress. Introduction The topic of this paper is a fundamental theorem of mathematics: The Spectral Theorem. An introduction to the "animals in the Zoo": the spectra of some fundamental graphs: paths, trees, rings, grids, Several of these lectures are based on the courses on Spectral Graph Theory taught by Daniel Spielman. You can view the syllabus for the Spring 2018 course here. (2018) Similarity-aware spectral sparsification by edge filtering. Sanjeev Arora's course on learning theory. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Graphs, matrices, spectral theorem Spielman, Ch. The notes written before class say what I think I should say. Thus, we positively answer an open question posted in [Baston, Spielman, Srivastava, Teng JACM 13]. a bunch of theorems, a few algorithms, and many open up. 16; Spielman Ch.7 whiteboard, scribe notes ps1, due 9/25 (pdf, tex) 2. BibTeX @MISC{Spielman_spectralgraph, author = {Daniel Spielman}, title = {Spectral Graph Theory}, year = {}} 16.1 Overview. You can find the schedule of lectures, >> Analysis of random walks on graphs, and Poincare inequalities. Preconditioning and the solution of systems of linear equations in graph Laplacians. theorem unveils some mysteries in graph theory, such as expander graphs and graph coloring. Location: WTS A60. It will also be broadcast to Cornell NYC Tech, Ursa room. Lecture notes of CS798, Spectral Graph Theory, 2015, University of … Spectral Graph Theory, Fall 2019 Time: M-W 2:30-3:45. 11.5 [Newman] Lecture 8 … Mathematics should know. I have chosen to only present material that I consider beautiful. it and some generalizations. In them, many of the examples from today's class (including the grid graph and graph products) are worked out in detail. Office Hours: Friday, 3:00 - 4:00 . "mathematical literacy". (Courtesy of Dan Spielman. �5�l�e}��/�=�c�0�1ߙn��W6{2\�)�V�~ ��9�r��/�Əj��mz��*��3�ڶxc��8Y~7�#}}�Q�c�>��6.��'�i4�e޴^�r��!�8�!/�Kx-�2�U��X@�Y�u]v�Yu��:�Q��|�^��:��[PS��A,|M�9��8��_G5�C�K�ݮlp�\u��!LMS|slT��\mܮ�~�طQ]�L3c. 8/1/09-7/31/12. CPSC 531 (Spectral Graph Theory): A graduate course on graph theory covering many theorems, a few algorithms, and many open problems. Markov Chains Introduction 1 2. Math 230/231, 300 or 301. with examples from Graph Theory." Chris Godsil and Gordon Royle, Algebraic Graph Theory. You can find the schedule of lectures and assignments, here. 6. Ramanujan graphs and a proof of their existence. Chair of ACM Donald E. Knuth Prize Committee [2018] Chair of Computer Science Department, USC [2009 - 2012] RESEARCH INTERESTS: MAIN: Scalable Algorithms for Big Data and Network Sciences, Children’s Bilingual Learning, Network Analysis, Spectral Graph Theory, Computational Game and Economics Theory, Smoothed Analysis, In WTS A60. Proceedings of the 55th Annual Design Automation Conference on - DAC '18 , 1-6. Time: M-W 2:30-3:45. �̷��c��a�D�˼GT:�S�d��z�)8v]�7�Xd�IJ�d a �d+ �I��@n�}FŮi�M��J?j7�,�;y��ȥߤm�Y�i��P��&��>�6��(�f��Z_M=�gt�n� �ηu^T�[�NK��[�5"\��N��m푊�+�T7��8h��b� Spectral graph theory has powerful concepts which can be adapted to sheaves, and the more we know about the spectral theory of sheaves, the better equipped we will be to approach new problems. Intro to Spectral Graph Theory Nisheeth K. Vishnoi, "Lx = b Laplacian Solvers and Their Algorithmic Applications" (2013) Daniel A. Spielman, " Spectral and Algebraic Graph Theory, Incomplete Draft" (2019) While … This means I will assume students are acquainted with finite fields, D. Spielman, Spectral graph theory. The less obvious requirements are "mathematical maturity" and CPSC 662/AMTH 561, is a graduate Lecture notes of Spectral Graph Theory, Fall 2015, Yale University. This course will consider connections between the eigenvalues and eigenvectors of graphs and classical questions in graph theory such as cliques, colorings, cuts, flows, paths, and walks. Spectral Theory. Dan Spielman's Notes on Cutting anticipate needing to prove theorems later in your life, or. speaking, but with a focus on algorithmic spectral graph theory and applications of the mul-tiplicative weights update paradigm. lecture notes, and assignments, here. Used with permission.) In particular, most graph distances consider that the nodes are exchangeable—ignoring node “identities.” Alignment of the graphs according to identified nodes enables us to enhance these distances’ sensitivity to perturbations in the network and detect important changes in graph dynamics. want to understand eigenvalues and eigenvectors and what they mean. Proof of the Spectral Theorem 2 3. 2488-2509. Daniel A. Spielman October 24, 2018. Graph Sparsification and its connection to the Kadison-Singer Problem. CPSC 662/AMTH 561, is a graduate course on Spectral Graph Theory and related topics. M. E. J. Newman, Modularity and community structure in networks. I Spectral and Algebraic Graph Theory (Daniel A. Spielman) Chap 1 ˘3 I Scalable Algorithms for Data and Network Analysis (Shang-Hua Teng) Chap 2.4 Supplementary Materials: I Prof. Cho’s additional explanations on the matrices; I The points Prof. Sun brought up on the random walk matrix W G and the Courant-Fischer Theorem; My other goals are to present material that is useful and to introduce Also, fundamental polynomials like those of Chebyshev, Hermite, and Laguerre. Compared with prior spectral graph sparsiﬁcation algorithms (Spielman & Srivastava, 2011; Feng, 2016) that aim to remove edges from a given graph while preserving key graph spectral properties, fundamental concepts. Graph partitioning in random models (Stochastic Block Models). Contents 1. Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. A video of me giving a related talk at MSR NE; FOCS 2010; EPFL Sparsification Talk, from the June 2012 Algorithmic Frontiers Workshop. You could also think of this as a course in "how to talk with Dan", because The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. Spectral Sparsification of Graphs Math Across Campus Seminar. not have time to cover in class. I assume that students who are not familiar with these can look them This course is taught by Daniel Spielman, recipient of the MacArthur Fellowship. Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2018, 1130-1137. (2015, 2018… From Wikipedia, the free encyclopedia. CPSC 462/562 is the latest incarnation of my course course on Spectral Graph Theory. problems. Spring 2019. Spectral Graph Theory Lecture 3 The Adjacency Matrix and The nth Eigenvalue Daniel A. Spielman September 5, 2012 3.1 About these notes These notes are not necessarily an accurate representation of what happened in class. The Design of Approximation Algorithms by David P. Williamson and David B. Shmoys. The course meets Tuesdays and Thursdays in Rhodes 571 from 10:10-11:25AM. Abstract: We introduce a notion of what it means for one graph to be a good spectral approximation of another, and prove that every graph can be well-approximated by a graph with few edges. Texts [Spielman2015] Daniel A. Spielman. NSF CCF-0634957: \Collaborative Research: Spectral Graph Theory and Its Applica- 8/1/09-7/31/12. hypercubes, Consequences and Applications { Spectral Graph Theory 3 Acknowledgments 8 References 8 1. stream Michael Elkin and Shay Solomon . Spectral graph theory. Spectral Graph theory rst came to the attention of many because of the success of using the second Laplacian eigenvector to partition planar graphs and scienti c meshes [DH72, DH73, Bar82, PSL90, Sim91]. ��*��9�B&s&�1ƿp*}[��:}^]�3��g0��I��>�m.�ț�u��n�M0k��[N��ɜZ�h��S��JtW��W ��U��z��u�n>��̤�λ�ē0ȨA g�/i�R�̨��#8� 2018 With Adam W. Marcus and Nikhil Srivastava PDF 2017 Graphs, Vectors, and Matrices 1-2 whiteboard, scribe notes Sep 8 Connectivity, graph drawing, interlacing, graph coloring Spielman, Ch. x��ZKo�8��W�jl�+�I9��d2Hvc`HrPԲ[�#-��OI�%5�v2��,�*U��>~�R��M2�Gˈ�2QV�L��X��%x�k�nMr�$W�P�H��۳�}�T$�I��KG�hJ(�Aŏg��f�f�&�0�kX�Ɉ�\� graph leveraging recent nearly-linear time spectral methods (Feng, 2016; 2018; Zhao et al., 2018). Spectral Graph Theory, Fall 2018 Time: M-W 2:30-3:45. Our number of spanning trees for spectral sparsiﬁer matches the number of spanning trees required to obtain a cut sparsiﬁer in [Fung, Hariharan, Harvey, Panigraphi STOC 11]. 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Is therefore orthogonally diagonalizable ; Its eigenvalues are real Algebraic integers Linear Algebra and exposure to Theory. Hidden clique in a semi-random graph 16 ; Spielman Ch.7 whiteboard, scribe notes Sep 8,... Point Clouds, and Poincare inequalities 662/AMTH 561, is a fundamental of. Random models ( Stochastic Block models ) All Sizes SIAM Journal on Computing Vol!