Lectures related to Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

Introduces elementary graph algorithms, focusing on Breadth-First Search and Depth-First Search.

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

Explores topological sort, acyclic graphs, Strongly Connected Components, magic algorithm, component graph, flow networks, and their applications.

Shortest Path Algorithms: BFS and Dijkstra

Explores Breadth-First Search and Dijkstra's algorithm for finding shortest paths in graphs.

Algorithmic Paradigms for Dynamic Graph Problems

Covers algorithmic paradigms for dynamic graph problems, including dynamic connectivity, expander decomposition, and local clustering, breaking barriers in k-vertex connectivity problems.

Integer Programming and Network Flows

Covers the fundamentals of integer programming and network flows in directed graphs.

Convergence of Random Walks

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

Cheeger's Inequalities

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