Spectral Graph Theory CMU

Welcome to our reading group. An initial, suggestive list of topics that we will mainly focus on,
are the following:

  • Spectral Graph Theory
  • Linear Systems
  • Cuts and Partitioning
  • Preconditioning

Resources

  • preconditioners.com
    link

Papers


An initial reading list, which will be "enriched" on the way:
  • Spectral Sparsification of Graphs link
    Daniel Spielman, Shang-Hua Teng
  • Twice-Ramanujan Sparsifiers link
    Joshua Batson, Daniel Spielman, Nikhil Srivastava
  • Graph Sparsification by Effective Resistances link
    Daniel Spielman, Nikhil Srivastava
  • Spectral Partitioning of Random Graphs link
    Frank McSherry
  • Spectral Partitioning Works: Planar graphs and finite element meshes link
    Daniel Spielman, Shang-Hua Teng
  • On the Performance of Spectral Graph Partitioning Methods. pdf
    Stephen Guattery, Gary Miller
  • Finding effective support-tree preconditioners. pdf
    Bruce M. Maggs, Gary Miller, Ojas Parekh, R. Ravi, and Shan Leung Maverick Woo
  • Performance Evaluation of a Parallel Preconditioner. pdf
    K.D Gremban, Gary Miller, M. Zagha
  • Spectral Rounding with Applications in Image Segmentation and Clustering pdf
    David Tolliver, Gary Miller
  • The diameter and Laplacian eigenvalues of directed graphs pdf
    Fan Chung
  • Graph partitioning into isolated, high conductance clusters: Theory, computation and applications to preconditioning. pdf
    Ioannis Koutis, Gary Miller
  • A linear work, O(n^{1/6}) parallel time algorithm for solving planar Laplacians. link
    Ioannis Koutis, Gary Miller
  • Combinatorial and algebraic tools for optimal multilevel algorithms. pdf
    Ioannis Koutis
  • Fast Computation of Low Rank Matrix Approximations pdf
    Dimitris Achlioptas, Frank McSherry