Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note,  demonstrate that the problem of "many-to-one matching with (strict) preferences over colleagues" is actually more difficult than the classical many-to-one matching problem, "matching without preferences over colleagues."  give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of "matching without preferences over colleagues," for any set of preferences. Our construction directly extends to generalized matching settings.
['Scott Duke Kominers']
I am writing a research paper on a idea Matching with preferences over colleagues solves classical matching
[{"from": "human", "value": "I am writing a research paper on a idea Matching with preferences over colleagues solves classical matching"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In this note,  demonstrate that the problem of \"many-to-one matching with (strict) preferences over colleagues\" is actually more difficult than the classical many-to-one matching problem, \"matching without preferences over colleagues.\"  give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of \"matching without preferences over colleagues,\" for any set of preferences. Our construction directly extends to generalized matching settings."}]