Graph Partitioning and Expanders - Stanford University

NovoEd
Online

Kostenlos

Wichtige informationen

  • Kurs
  • Online
  • Wann:
    Freie Auswahl
Beschreibung

  The following course, offered by NovoEd, will help you improve your skills and achieve your professional goals. During the program you will study different subjects which are deemed to be useful for those who want to enhance their professional career. Sign up for more information!

Wichtige informationen
Veranstaltungsort(e)

Wo und wann

Beginn Lage
Freie Auswahl
Online

Was lernen Sie in diesem Kurs?

Algorithms
Mathematics
Maths
Programming
Graph

Themenkreis

In this research-oriented graduate course, we will study algorithms for graph partitioning and clustering, constructions of expander graphs, and analysis of random walks. These are three topics that build on the same mathematical background and that have several important connections: for example it is possible to find graph clusters via random walks, and it is possible to use the linear programming approach to graph partitioning as a way to study random walks.

We will study spectral graph theory, which explains how certain combinatorial properties of graphs are related to the eigenvalues and eigenvectors of the adjacency matrix, and we will use it describe and analyze spectral algorithms for graph partitioning and clustering. Spectral graph theory will recur as an important tool in the rest of the course. We we will also discuss other approaches to graph partitioning via linear programming and semidefinite programming. Then we will study constructions of expander graphs, which are graphs with very strong pseudorandomness properties, which are useful in many applications, including in cryptography, in complexity theory, in algorithms and data structures, and in coding theory. Finally, we will study the mixing time of random walks, a problem that comes up in several applications, including the analysis of the convergence time of certain randomized algorithms, such as the Metropolis algorithm.


Workload 

about 8 hours per week


Prerequisites 

linear algebra, discrete probability, and algorithms

Zusätzliche Informationen

The Instructor Luca Trevisan Professor of Computer Science, Stanford University