Lectures related to Bellman-Ford Algorithm: Analysis and Correctness

Graph Algorithms II: Traversal and Paths

Explores graph traversal methods, spanning trees, and shortest paths using BFS and DFS.

Dynamic Programming: Shortest Paths Algorithms

Explores dynamic programming strategies for finding shortest paths in networks with various algorithms and complexities.

Shortest Paths: Bellman-Ford and Dijkstra

Covers the Bellman-Ford and Dijkstra algorithms for finding shortest paths in graphs with different edge weights.

Dijkstra's Algorithm and Shortest Path

Covers Dijkstra's algorithm for shortest path problems and its application in ALL-TO-ONE and ALL-PAIRS algorithms.

Dijkstra's Algorithm Overview

Demonstrates the iterative process of applying Dijkstra's algorithm to find optimal paths.

Minimum Spanning Trees: Prim's Algorithm

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

Dijkstra's Algorithm and Probabilistic Analysis

Introduces Dijkstra's algorithm and probabilistic analysis through the Hiring Problem.

Shortest Path Algorithms: BFS and Dijkstra

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

Shortest Paths: Negative Weights

Explores Bellman-Ford algorithm for negative weight graphs and currency exchange rates.

Shortest Paths: Negative Weights & Applications

Covers Minimum Spanning Trees, Kruskal's Algorithm, and Shortest Paths in directed graphs.

Networked Control Systems: Opportunities

Explores coordination in networked control systems, graph theory, and consensus algorithms.

Bellman-Ford Algorithm: Shortest Path Estimation

Explains the Bellman-Ford algorithm for finding the shortest path in a directed graph with edge weights.

Introduction to Shortest Path

Introduces the concept of shortest path, discussing weighted paths, Hamiltonian paths, and path optimization algorithms.

Unweighted Bipartite Matching

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

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.

Cheeger's Inequalities

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

Graph Theory and Network Flows

Introduces graph theory, network flows, and flow conservation laws with practical examples and theorems.

Max Sum Diversification

Explores maximizing diversity in document selection, graph clique determination, theorems on negative type, and convex optimization.

Bellman-Ford Algorithm: Shortest Path

Provides an example of the Bellman-Ford algorithm for finding the shortest path in a graph.

Dynamic Programming: Pascal's Triangle & Floyd's Algorithm

Explores dynamic programming through Pascal's Triangle and Floyd's Algorithm.