PPT-Resparsification of Graphs

Richard Peng Georgia Tech Rasmus Kyng Yale Sushant Sachdeva Google U of Toronto Jakub Pachocki Harvard Graph Sparsification The Resparsification Game Concentration bounds Matrix Martingales. There is actually only one main program the spe ci64257c layout algorithms implemented as plugins Thus the yl ar gely share all of the same commandline options dot draws directed graphs It works well on D AG sa nd other graphs that can be drawn as h Anthony Bonato. Ryerson University. CanaDAM. 2011. Cop number of a graph. the . cop number of a graph. , written . c(G). , is an elusive graph parameter. few connections to other graph parameters. hard to compute. Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . Network Science: Random Graphs . 2012. Prof. Albert-László Barabási. Dr. Baruch Barzel, Dr. Mauro Martino. RANDOM NETWORK MODEL. Network Science: Random Graphs . 2012. Erdös-Rényi model (1960). Isabelle Stanton, UC Berkeley. Gabriel . Kliot. , Microsoft Research XCG. Modern graph datasets are huge. The web graph had over a trillion links in 2011. Now?. . facebook. has “more than 901 million users with average degree 130”. 2-3. In addition to the histogram, the frequency polygon, and the . ogive. , several other types of graphs are often used in statistics. They are the bar graph, Pareto chart, time series graph, and pie chart. . Masaru . Kamada. Tokyo . University of . Science. Graph Theory Conference. i. n honor of Yoshimi . Egawa. on the occasion his 60. th. birthday. September 10-14, 2013. In this talk, all graphs are finite, undirected and allowed multiple edges without loops.. L. á. szl. ó. . Lov. á. sz. Eötvös Loránd University. Budapest . September 2012. 1. September 2012. Tur. á. n’s Theorem . (special case proved by Mantel):. . G. contains no triangles .  #edges. Daniel A. Spielman. Yale University. AMS Josiah Willard Gibbs Lecture. January . 6. , 2016 . From Applied to Pure Mathematics. Algebraic and Spectral Graph Theory. . . Sparsification. :. a. pproximating graphs by graphs with fewer edges. Misleading Graphs. Good . graphs are extremely powerful tools for displaying large quantities . of complex . data; they help turn the realms of information available today . into knowledge. . But, unfortunately, some graphs deceive or mislead. This . Minors, . Bidimensionality. ,. & Decomposition. r. r. Erik Demaine. MIT. Goals. How far . beyond planar graphs . can we go?. Graphs excluding. a fixed minor. Powers thereof. Build . general approximation frameworks . Graphs.  . Graphs . capture . much more detail than numerical summaries, so very useful for learning about data and communicating its features.. At the same time, graphical interpretation isn’t standard in the way that numerical summaries are, and our eyes can fool us.. Eyal. Ackerman. University of Haifa and . Oranim. College. Drawing graphs in the plane. Consider drawings of graphs in the plane . s.t. .. No loops or parallel edges. Vertices .  distinct points. Section . 10.3. Representing Graphs: . Adjacency Lists. Definition. : An . adjacency list . can be used to represent a graph with no multiple edges by specifying the vertices that are adjacent to each vertex of the graph..