I am currently working on implementing the minimum-weight perfect matching problem for a fully connected graph with an even number of vertices. The goal is to pair the vertices in a way that minimizes the total sum of weights between paired vertices.
I have been researching the topic, but most of the available information consists of scientific research papers, which are not providing simple explanations or implementation examples.
I am wondering if there is an alternative algorithm that I could use to solve this problem in a simpler manner. Would it be feasible to implement a greedy algorithm for this purpose? I am looking for guidance or suggestions on how to approach the implementation of this problem. Any explanation or example code would be greatly appreciated. Thank you.