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. for Linear Algebra and Beyond. Jim . Demmel. EECS & Math Departments. UC Berkeley. 2. Why avoid communication? (1/3). Algorithms have two costs (measured in time or energy):. Arithmetic (FLOPS). Communication: moving data between . 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. Yiannis Koutis, Gary Miller. Carnegie Mellon University . TexPoint. fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. Where I am coming from. Theoretical Computer Science Community. Amrinder Arora. Permalink: http://standardwisdom.com/softwarejournal/presentations/. Summary. Online algorithms show up in . many. practical problems.. Even if you are considering an offline problem, consider what would be the online version of that problem.. Lecture 23. a. acyclic with neg. weights (topological sort algorithm). 8/25/2009. 1. ALG0183 Algorithms & Data Structures by Dr Andy Brooks. “The shortest-path algorithms are all . single-source algorithms. Hao Wei. 1. , . Jeffrey Xu Yu. 1. , Can L. u. 1. , . Xuemin. Lin. 2. . 1 . The . Chinese University of Hong Kong, Hong Kong. 2 . The . University of New South Wales. , . Sydney, Australia. Graph in Big Data . 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. 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.. 10 Bat Algorithms Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, 2014 The bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010. 10.1 Echolocation of Bats Lecture . 17: More . Dijkstra. ’s. and. Minimum Spanning Trees. Aaron Bauer. Winter 2014. Dijkstra’s. Algorithm: Idea. Winter 2014. 2. CSE373: Data Structures & Algorithms. Initially, start node has cost 0 and all other nodes have cost .