Hello everyone. Can anyone tell me a real-life problem I've encountered: Summary: Given a graph consisting of 2N vertices and M weighted edges. Find a way to pair N pairs of vertices such that the maximum value of N paired pairs is the smallest.

I have tried to find the optimal solution in polynomial time but can't find it. I plan to use binary search and then recursively go back and forth to generate all possible cases and then get min. Please give me keywords or answers. Sorry for my bad english.

input: 4 10 1 3 4 1 4 3 1 5 2 2 4 5 3 6 1 7 4 3 7 2 1 6 1 3 8 5 5 6 8 3 output: 5