Lectures related to Shortest Path Problems: Bellman-Ford

Introduction to Shortest Path

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

Causal Inference: Front Door Criterion

Explains the front door criterion in causal inference and its sufficient conditions for variables blocking paths effectively.

Ising Model: 2D Expansion

Explores the Ising model in 2D, emphasizing system expansion and properties.

Dijkstra's Algorithm: All-Pairs

Covers Dijkstra's algorithm and its application to the all-pairs shortest path problem.

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.

Bellman Ford Algorithm

Explores the Bellman Ford algorithm for finding the shortest path in graphs with negative edge weights.

Shortest path, Longest path

Explores the implications of transforming a shortest path problem into a longest path problem in optimization.

Theory of Computation: NP Problems Examples

Examines NP problems, graph coloring, path optimization, and computational complexity distinctions in P and NP classes.

Complex Systems: Critical Phenomena

Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Shortest Path in Directed Graphs

Covers finding the shortest path in directed graphs efficiently using algorithmic approaches and discussing related NP-complete problems.

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.

Shortest Path: Introduction

Covers one-to-one shortest path, negative cost edges, and optimal solutions.

Transhipment and Shortest Paths

Covers optimality conditions, total unimodularity, and algorithms for transhipment problems.

Optimization Problems: Path Finding and Portfolio Allocation

Covers optimization problems in path finding and portfolio allocation.

Dynamic Programming: Shortest Paths Algorithms

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

Graph Algorithms II: Traversal and Paths

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

Shortest Paths: Negative Weights

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

Shortest Paths: Bellman-Ford and Dijkstra

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

Shortest Path Algorithms: BFS and Dijkstra

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

Shortest Paths: Negative Weights & Applications

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