Graph Algorithms: BasicsIntroduces the basics of graph algorithms, covering traversal, representation, and data structures for BFS and DFS.
Max-flow and Disjoint SetsExplores the Ford-Fulkerson method, max-flow, applications of max-flow, and the disjoint-set data structure.
DFS Continuation: Topological SortCovers topics like DFS output, edge classification, acyclic graphs, correctness, time analysis, SCCs, and the Topological Sort algorithm.
Polynomial Identity TestingCovers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
Sparsest Cut: ARV TheoremCovers 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.