first dropping the link that will serve as reference: NRMP Residency Matching
I have a sort of side project (nothing riding on it, computational performance not an issue, so feel free to go wild, I love learning new things) and I am attempting to match members of group L to members of group B. All members will provide a list (potentially incomplete) of the members in the other group, ordered by preference (ranked list). The groups are not necessarily equal in size, with B generally being larger than L.
Potential Twist!: How about allowing each other member of group B to provide a list of who they consider as best Li for Bi (best member of group L for each member of group B)? Does this make the situation more interesting? Yes, power play struggles by intentionally throwing off rankings would count as interesting here ;)
This, from my limited Googling due to near-zero domain knowledge, appears to be closely related to the Stable Marriage Problem, which appears to be the algorithm used in the above given NRMP algorithm.
Note I have already seen this question, which is close, but not quite right, with score versus rankings making it a completely different question (in my mind at least...is it?)
- I am not well versed at formal mathematics at all (engineer here), so what is this type of problem called?
- What category does it fall under? (Graph, etc or is that what category a solution would fall under?)
- What concrete conclusions can we derive from the algorithm? (Is it optimal? -SMP is, but with differing sized groups, is it? Does order of members passed through the algorithm affect the outcome in any way?)
- Is there a better (more efficient in my circumstance, cooler, newer, technically outrageous but mathematically more interesting) way to do this? Implementing this is meant to be entertainment for me - real cool right? - so no restrictions really.
P.S. A crazy idea I had - introducing a questionnaire, providing features that can then be used in a fuzzy classification system for matching???
EDIT: I've been lurking here a while and realize that people here are much smarter than me, so feel free to stretch the question's restrictions within reason and have fun with it. (IE a small group F overseeing the matching system may have more influence on the outcome in case of conflicts)