Marriage Problem: Gale Shapley Algorithm

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Handling Network Data

Covers handling network data, types of graphs, centrality measures, and properties of real-world networks.

Unweighted Bipartite Matching

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

The Marriage Problem

Explores the marriage problem, modeling the process as a controlled stochastic process with dynamic programming algorithms to find the optimal policy for accepting bachelors.

Bipartite Graphs: Independent Sets

Explores bipartite graphs, independent sets, Shearer's Lemma, labeled graphs, and entropy analysis.

Statistical Analysis of Network Data

Introduces network data structures, models, and analysis techniques, emphasizing permutation invariance and Erdős-Rényi networks.

Szemerédi Regularity Lemma

Explores the Szemerédi Regularity Lemma, e-regularity in bipartite graphs, supergraph structure, and induction techniques.

Expander Graphs: Properties and Eigenvalues

Explores expanders, Ramanujan graphs, eigenvalues, Laplacian matrices, and spectral properties.

Linear Programming Duality

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

Graph Algorithms: Flows and Strongly Connected Components

Discusses graph algorithms, focusing on flow networks and strongly connected components.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

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