Graph Algorithms: Ford-Fulkerson and Strongly Connected Components

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Graph Algorithms: Modeling and Representation

Covers the basics of graph algorithms, focusing on modeling and representation of graphs in memory.

Fixed Points in Graph Theory

Focuses on fixed points in graph theory and their implications in algorithms and analysis.

Max-flow and Disjoint Sets

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

Connectivity in Graph Theory

Covers the fundamentals of connectivity in graph theory, including paths, cycles, and spanning trees.

DFS Continuation: Topological Sort

Covers topics like DFS output, edge classification, acyclic graphs, correctness, time analysis, SCCs, and the Topological Sort algorithm.

Minimum Spanning Trees: Prim's Algorithm

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Polynomial Identity Testing

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

Flow Networks: Strongly Connected Components

Introduces Strongly Connected Components and Flow Networks, discussing algorithms and applications.

Graphs: Properties and Representations

Covers graph properties, representations, and traversal algorithms using BFS and DFS.

Sparsest Cut: ARV Theorem

Covers 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.