Lecture 1: Electrical Flows as a New Primitive for Graph Algorithms
Lecture 2: Approximating Maximum Flow with Electrical Flows
Lecture 3: Maximum Flows and Interior-point Methods

This series of talks was part of the Algorithmic Spectral Graph Theory Boot Camp. Videos for each talk are available through the links above.

Speaker: Aleksander Mądry, École Polytechnique Fédérale de Lausanne

Graphs are ubiquitous in all modern sciences. This motivates a need for algorithmic tools that are capable of analyzing and computing on graphs in an efficient manner. A need that is even more pressing now that the graphs we are dealing with tend to be massive, rendering traditional methods no longer adequate. 

In this talk, I will discuss a recent progress on the maximum flow problem and use it as an illustration of a broader emerging theme in graph algorithms that employs optimization methods as an algorithmic bridge between our combinatorial and spectral understanding of graphs. 

I will also briefly outline how this line of work brings a new perspective on some of the core continuous optimization primitives - most notably, interior-point methods.