This video explores the Traveling Salesman Problem, and explains two approximation algorithms for finding a solution in polynomial time. The first method explained is a 2-approximation that uses a minimum spanning tree (MST) and depth first search (DFS). The second method is Christofides' algorithm, which combines perfect matching with a minimum spanning tree. TSP is a classic NP-Hard problem.
I recommend you first watch the following videos on MSTs and DFS, which I reference in this video:
► Kruskal's Algorithm: https://youtu.be/Rc6SIG2Q4y0
► Prim's Algorithm, https://youtu.be/MaaSoZUEoos
► Depth First Search, https://youtu.be/tlPuVe5Otio
Some of my other related graph videos:
► Dijkstras Intro https://youtu.be/U9Raj6rAqqs
► Dijkstras on Directed Graph https://youtu.be/k1kLCB7AZbM
► Bellman-Ford https://youtu.be/dp-Ortfx1f4
► Bellman-Ford Example https://youtu.be/vzBtJOdoRy8
► Floyd-Warshall https://youtu.be/KQ9zlKZ5Rzc
► Floyd-Warshall on Undirected Graph https://youtu.be/B06q2yjr-Cc
► Breadth First Search https://youtu.be/E_V71Ejz3f4