PPT-Graph Sparsifiers by Edge-Connectivity and

Random Spanning Trees Nick Harvey U Waterloo CampO Joint work with Isaac Fung TexPoint fonts used in EMF Read the TexPoint manual before you delete this box A A A What are sparsifiers. Implement a graph in three ways:. Adjacency List. Adjacency-Matrix. Pointers/memory for each node (actually a form of adjacency list). Adjacency List. List of pointers for each vertex. Undirected Adjacency List. This copyrighted material is taken from . Introduction to Graph Theory. , 2. nd. Ed., by Doug West; and is not for further distribution beyond this course.. These slides will be stored in a limited-access location on an IIT server and are not for distribution or use beyond Math 454/553.. Richard Peng. M.I.T.. OUtline. Structure preserving sampling. Sampling as a recursive ‘driver’. Sampling the inaccessible. What can sampling preserve?. Random Sampling. Collection of many objects. 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. Implement a graph in three ways:. Adjacency List. Adjacency-Matrix. Pointers/memory for each node (actually a form of adjacency list). Adjacency List. List of pointers for each vertex. Undirected Adjacency List. Michael Tarsi, Blavatnik School of Computer Science, Tel-Aviv University, Israel. The Polynomial Method. (Alon, T). The Graphic case. P. G=. . (x. i – . x. j) over all edges (i,j). E. A proper coloring of G  an assignment of “colors” to the . Sparsifiers. by. Edge-Connectivity and. Random Spanning Trees. Nick Harvey. University of Waterloo. Department of . Combinatorics. and Optimization. Joint work with Isaac Fung. TexPoint fonts used in EMF. . Michael Tarsi, Blavatnik School of Computer Science, Tel-Aviv University, Israel. The Polynomial Method. (Alon, T). The Graphic case. P. G=. . (x. i – . x. j) over all edges (i,j). E. A proper coloring of G  an assignment of “colors” to the . prepared and Instructed by. Shmuel Wimer. Eng. Faculty, Bar-Ilan University. The Friendship Theorem. May 2014. Connectivity. 2. Theorem. . (. Erdös. et. al. 1966) Let . be a simple, . -vertex graph, in which any two vertices (people) have exactly one common . Cluster Analysis. Outline. Introduction to Cluster Analysis. Types of Graph Cluster Analysis. Algorithms for Graph Clustering. k-Spanning Tree. Shared Nearest Neighbor. Betweenness Centrality Based. Highly Connected Components. Rashid Kaleem. 1. , . Anand. Venkat. 2. , . Sreepathi. Pai. 1. , Mary Hall. 2. , . Keshav. Pingali. 1. 1. University . of Texas at Austin. 2. University of Utah. Outline. Stochastic Gradient Descent. Adjacency List. Adjacency-Matrix. Pointers/memory for each node (actually a form of adjacency list). Adjacency List. List of pointers for each vertex. Undirected Adjacency List. Adjacency List. The sum of the lengths of the adjacency lists is 2|E| in an undirected graph, and |E| in a directed graph.. Distributed Graph Analytics. Loc Hoang               Roshan Dathathri. Gurbinder Gill                Keshav Pingali. 1. Distributed Graph Analytics. Analytics on unstructured data. Finding suspicious actors in crime networks. Just a PC. Aapo Kyrölä . akyrola@cs.cmu.edu. Carlos . Guestrin. University of . Washington & CMU. Guy . Blelloch. CMU. Alex . Smola. CMU. Dave Andersen. CMU. Jure . Leskovec. Stanford. Thesis Committee:.