Matching Polynomials: Real-Rootedness and Signings

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Related lectures (19)

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

Interlacing Families and Ramanujan Graphs

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Ramanujan Graphs: Constructions and Similarities

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

Linear Programming Duality

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

Greedy Change-Making Algorithm: Optimality and Stability

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

Unweighted Bipartite Matching

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

Matroids: Matroid Intersection

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

Algorithms & Growth of Functions

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

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.