Graph Sketching: Connected Components

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Related lectures (27)

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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.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Approximation Algorithms

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

Generalization Error

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Cheeger's Inequalities

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

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Unweighted Bipartite Matching

Introduces unweighted bipartite matching and its solution using linear programming and the simplex method.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.