I'm not a mathematician so it's possible that I'm using incorrect terminology here, but I'll try to explain.
Say I have an arbitrary evenly sized list of variables (for instance, A to H). Each of these variables has a value representing its relationship to each of the other variables individually. A variable cannot have a relationship with itself, so those values are represented as N/A. Below is a matrix showing the relationship between these example variables.
Matrix of values relating to each pair of variables A through H.
Assuming that each variable cannot be paired with itself, and no variable can be paired with another variable twice, how could I find the 'optimal' pairs between each variable that would result in the highest (or lowest) total cumulative score? For instance, according to the above image:
- AB = 1
- CD = 1
- EF = 0
- GH = 1
Total score = 3
- AG = 9
- BF = 6
- CE = 8
- DH = 9
Total score = 32
It's possible that this problem is related to Mutual Coherence, but I can't say that for sure since I'm having a bit of trouble comprehending that explanation of the concept.
What you are looking for is a maximum (or minimum) weighted matching. There are a number of ways to solve this. The Hungarian algorithm is particularly helpful.