Sorted Edges Algorithm (a.k.a. Cheapest Link Algorithm) Explained | Graph Theory

In this video, I break down the Sorted Edges Algorithm (also known as the Cheapest Link Algorithm), a method used in Graph Theory to solve problems like the Traveling Salesman Problem by finding the shortest possible circuit.

Here’s a summary of the steps covered in this tutorial:

1. Select the cheapest unused edge: We start by picking the edge with the smallest weight in the graph.
2. Add the cheapest unused edge: Continue adding edges to the circuit, with two exceptions: a. Avoid incomplete circuits: Don't add an edge if it would create a circuit that doesn’t pass through all vertices. b. Vertex degree check: Don’t add an edge if it would give any vertex a degree of 3.
3. Repeat until complete: Continue selecting and adding edges until a full circuit containing all vertices is formed.

By following these steps, you'll be able to apply the Sorted Edges Algorithm to efficiently solve various optimization problems in graph theory. If you have any questions or need further clarification, feel free to drop a comment below!

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. Original text from Math in Society by David Lippman.