SPEAKER: Richard Peng
Department of Computer Science
Carnegie Mellon University
TITLE: Algorithm Design Using Spectral Graph Theory
Spectral Graph Theory is the interplay between linear algebra and combinatorial graph theory. One application of this interplay is fast solvers for symmetric diagonally dominant (SDD) linear systems, which occur ubiquitously in combinatorial optimization, computer vision, computer graphics and machine learning.
This talk will present an algorithm for solving SDD linear systems with m non-zero entries to an error of at most epsilon in O(m log n log(1/epsilon)) expected time. The solver algorithm is based on a multitude of tools developed over the past decade. At the heart of it is an algorithm that efficiently finds a chain of increasingly sparser graphs that are spectrally 'equivalent', which may be of independent interest.
I will also describe recent work on using the solver for total variation minimization and undirected multicommodity flow. As well as mention results about speeding up and parallelizing one of the key underlying routines.
Topics in this talk represent joint work with Guy Blelloch, Anupam Gupta, Jon Kelner, Yiannis Koutis, Aleksander Madry, Gary Miller and Kanat Tangwongsan.