Lectures on Algorithmic Spectral Graph Theory
نویسنده
چکیده
منابع مشابه
CS 168 : The Modern Algorithmic Toolbox Lectures # 17 and # 18 : Spectral Graph Theory
Most of our lectures thus far have been motivated by concrete problems, and the problems themselves led us to the algorithms and more widely applicable techniques and insights that we then went on to discuss. This section has the opposite structure: we will begin with the very basic observation that graphs can be represented as matrices, and then ask “what happens if we apply the linear algebra...
متن کاملCS 168 : The Modern Algorithmic Toolbox Lectures # 11 and # 12 : Spectral Graph Theory
Most of our lectures thus far have been motivated by concrete problems, and the problems themselves led us to the algorithms and more widely applicable techniques and insights that we then went on to discuss. This section has the opposite structure: we will begin with the very basic observation that graphs can be represented as matrices, and then ask “what happens if we apply the linear algebra...
متن کاملLectures on Spectral Graph Theory
Contents Chapter 1. Eigenvalues and the Laplacian of a graph 1 1.1. Introduction 1 1.2. The Laplacian and eigenvalues 2 1.3. Basic facts about the spectrum of a graph 6
متن کاملReferences on Higher Laplacian Eigenvalues and Combinatorial Graph Properties
This is a collection of references for a series of lectures that I gave in the “boot camp” of the semester on spectral graph theory at the Simons Institute in August, 2014. To keep this document focused, I only refer to results related to the lectures in question, which means that my own work is disproportionally represented. I plan to post a better version of this document in the future, so pl...
متن کاملCourant-Fischer and Graph Coloring
4.1 Eigenvalues and Optimization I cannot believe that I have managed to teach three lectures on spectral graph theory without giving the characterization of eigenvalues as solutions to optimization problems. It is one of the most useful ways of understanding eigenvalues of symmetric matrices. To begin, let A be a symmetric matrix with eigenvalues α1 ≥ α2 ≥ · · · ≥ αn, and corresponding orthono...
متن کامل