Lectures in course CS-455: Topics in theoretical computer science

Cheeger's Inequality

Explores Cheeger's inequality and its implications in graph theory.

Analysis of ARV

Covers the analysis of ARV, focusing on minimizing distances between points in cutis vis.

Convergence of Random Walks

Explores the convergence of random walks on graphs and the properties of weighted adjacency matrices.

Cheeger's Inequalities

Explores Cheeger's inequalities for random walks on graphs and their implications.

Semi-Definite Programming

Covers semi-definite programming and optimization over positive semidefinite cones.

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Sparsest Cut: Leighton-Rao Algorithm

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Sparsest Cut: ARV Theorem

Covers the proof of the Bourgain's ARV Theorem, focusing on the finite set of points in a semi-metric space and the application of the ARV algorithm to find the sparsest cut in a graph.