Matroids: Matroid Intersection

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Related lectures (29)

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Unweighted Bipartite Matching

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

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

Discusses the Ford-Fulkerson method and strongly connected components in graph algorithms.

Polynomial Identity Testing

Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.

Algorithms: Union Find and Minimum Spanning Trees

Discusses Union-Find data structures and Minimum Spanning Trees, covering algorithms and their applications in network design and optimization.

Cheeger's Inequalities

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

Greedy Algorithms & Matroids

Introduces greedy algorithms and matroids, highlighting their efficiency in solving optimization problems.

Graph Sketching: Connected Components

Covers the concept of graph sketching with a focus on connected components.

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.

Convergence of Random Walks

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

Linear Programming Duality

Explores linear programming duality, covering constraints, variables, solutions, and the relationship between primal and dual LP.