TL;DR
This paper studies popular b-matchings in agent-house matching problems with capacities and preferences, providing characterizations, complexity results, and polynomial algorithms for specific cases.
Contribution
It offers a characterization of popular b-matchings, explores NP-hardness, and develops polynomial algorithms for certain variants.
Findings
Characterization of popular b-matchings
NP-hardness results for some versions
Polynomial algorithms for specific cases
Abstract
Suppose that each member of a set of agents has a preference list of a subset of houses, possibly involving ties and each agent and house has their capacity denoting the maximum number of correspondingly agents/houses that can be matched to him/her/it. We want to find a matching , for which there is no other matching such that more agents prefer to than to . (What it means that an agent prefers one matching to the other is explained in the paper.) Popular matchings have been studied quite extensively, especially in the one-to-one setting. We provide a characterization of popular b-matchings for two defintions of popularity, show some -hardness results and for certain versions describe polynomial algorithms.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Voting Systems · Complexity and Algorithms in Graphs · Auction Theory and Applications