Dividing a graph to triple-vertices graphs such the sum of weights of edges is minimized

Question

I want to divide a graph to subgraphs that each subgraph made from maximum 3 vertices and sum of weight of edges is minimized, the main graph is complete ( have all possible edges ), and edges are weighted. the main problem that i want to solve is finding close three threes points on a map.

Answer 1

I'm sure this problem is NP-Complete. It's called the minimum k-cut problem.

Try to take a look at this article. It talks about approximation algorithms to solve such problems.