PPT-Sparsified Matrix Algorithms for Graph Laplacians

Richard Peng Georgia Tech OUtline Structured Linear Systems Iterative and Direct Methods Graph Sparsification Sparsified Squaring Speeding up Gaussian Elimination Graph Laplacians 1. Dominic Berry. Macquarie University. We want to simulate the evolution. The Hamiltonian is a . sum of terms:.  . Simulation of Hamiltonians. Seth Lloyd. 1996. We . can perform. For . short times . we . Lecture 18. The basics of graphs.. 8/25/2009. 1. ALG0183 Algorithms & Data Structures by Dr Andy Brooks. Watch out for self-loops in graphs.. 8/25/2009. ALG0183 Algorithms & Data Structures by Dr Andy Brooks. 1. Graph Algorithms. Many problems are naturally represented as graphs. Networks, Maps, Possible paths, Resource Flow, etc.. Ch. 3 focuses on algorithms to find connectivity in graphs. Ch. 4 focuses on algorithms to find paths within graphs. George Caragea, and Uzi Vishkin. University of Maryland. 1. Speaker. James Edwards. It has proven to be quite . difficult. to obtain significant performance improvements using current parallel computing platforms.. GraphBLAS. Jeremy Kepner, Vijay . Gadepally. , Ben Miller. 2014 December. This material is based upon work supported by the National Science Foundation under Grant No. DMS-. 1312831.. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.. Matrix. •. . Binary Matrix. •. . Sparse Matrix. •. . Operations for Vectors/Matrices. •. . Graph and Adjacent Matrix. •. . Adjacent List. Matrix and Graph. •. . Matrix is a 2-dimensional . Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Richard C. Wilson. Dept. of Computer Science. University of York. Graphs and Networks. Graphs . and. networks . are all around us. ‘Simple’ networks. 10s to 100s of vertices. Graphs and networks. Richard Peng. Georgia Tech. OUtline. (Structured) Linear Systems. Iterative and Direct Methods. (. Graph) . Sparsification. Sparsified. Squaring. Speeding up Gaussian Elimination. Graph Laplacians. 1. Richard Peng. Georgia Tech. Based on . recent works . joint with:. Serban . Stan (Yale. ), . Haoran. . Xu (MIT. ),. Shen . Chen Xu (CMU. ), . Saurabh. . Sawlani. (. GaTech. ). John . Gilbert (UCSB. John R. Gilbert (. gilbert@cs.ucsb.edu. ). www.cs.ucsb.edu/~gilbert/. cs219. Systems of linear equations:. . Ax = . b. Eigenvalues and eigenvectors:. Aw = . λw. Systems of linear equations: Ax = b. CIS 606. Spring 2010. Graph representation. Given graph . G. . = (. V. , . E. ). . In . pseudocode. , represent vertex set by . G.V . and edge . set by . G.E. .. G . may be either directed or undirected.. graphs and their representation in computers . Jiří Vyskočil, Radek Mařík. 201. 3. Introduction. Subject WWW pages. :. . https://cw.felk.cvut.cz/doku.php/courses/a. e. 4m33pal/start. Goals. . Individual implementation of variants of standard (basic and intermediate) problems from several selected IT domains with rich applicability. Algorithmic . Announcements. Talk on technical interviews . today!. Gugenheim. 220 at 1:10 PM.. Para Exercise feedback soon.. P2 Feedback (hopefully) Saturday.. Announcements. Please fill out course evaluations..