Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.
Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.
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.
Covers the basics of information theory, entropy, and fixed points in graph colorings and the Ising model.
Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.
