Optimizing Extremely Effective Minimum Spanning Trees The goal of my master's project is to create an algorithm that finds extremely efficient solutions in linear time. In a graph of size n, there are n^(n-2) spanning trees that are made up of both dominated and non-dominated trees.There are some extremely efficient and non-extremally efficient non-dominated solutions among all of them.

Extremal Efficient Solution Extremal efficient solutions are those that are located on the convex hull or on its boundary.

Non-Extremal Efficient Solution Non-extremal efficient solutions are those that are located inside the convex hull. They are essentially difficult to locate. In essence, we have developed an algorithm to identify every non-dominated solution, also referred to as the Pareto optimal solution. We are attempting to find a polynomial time algorithm to determine the subset of extremely efficient solutions that lie on the hull's boundary, but this algorithm is output sensetive, meaning complexity depends on the output set.