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 . 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 . 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. 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. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Outline. Min s-t cut problem. 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. 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 . 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 . Jim . Demmel. EECS & Math Departments. UC Berkeley. Why avoid communication? . Communication = moving data. Between level of memory hierarchy. Between processors over a network. Running time of an algorithm is sum of 3 terms:.