Lectures related to Fractional matching

Linear Programming Duality

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

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Unweighted Bipartite Matching

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

Polynomial Identity Testing

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

Matroids: Matroid Intersection

Covers the concept of matroids, focusing on matroid intersection and the properties of subsets of a ground set.

Algorithms: Stable Matchings

Covers the concept of stable matchings and the Gale-Shapley algorithm.

Algorithms: Stable Matchings

Covers the concept of stable matchings and the Gale-Shapley algorithm.

Max-flow Min-cut Theorem

Explores the Max-flow Min-cut theorem, integral capacities, Ford-Fulkerson method, bipartite matching, and edge-disjoint paths.

Ramanujan Graphs: Constructions and Similarities

Explores Ramanujan graphs' constructions, matching polynomials, perfect matchings, and universal covers, along with quantitation and qualitative aspects.

Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

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

Greedy Change-Making Algorithm: Optimality and Stability

Explores the optimality of the greedy change-making algorithm and the stability of maximum matching.

Matching Polynomials: Real-Rootedness and Signings

Explores matching polynomials, real-rootedness, signings, matchings sizes, and Hermann-Lieb condition.

Recent Advances in the Dimer Model and Its Applications

Covers recent advancements in the dimer model, emphasizing its applications in probability and conformal field theory.

Max-flow and Disjoint Sets

Explores the Ford-Fulkerson method, max-flow, applications of max-flow, and the disjoint-set data structure.

Marriage Problem: Gale Shapley Algorithm

Covers the Marriage Problem and the Gale Shapley Algorithm to find stable matches.

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.

Linear Programming: Weighted Bipartite Matching

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.

Comparing Hierarchical Clusterings

Covers the derivation and use of a measure of similarity between hierarchical clusterings, focusing on the Bk measure.