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- W2056576409 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 houses/agents (respectively) that can be matched to him/her/it. We want to find a matching M, called popular, for which there is no other matching M^' such that more agents prefer M^' to M than M to M^', subject to a suitable definition of ''prefers''. In the above problem each agent uses exactly one vote to compare two matchings. In the other problem we consider in the paper each agent has a number of votes equal to their capacity. Given two matchings M and M^', an agent compares their best house in matching M@?M^' to their best house in matching M^'@?M and gives one vote accordingly, then their second best houses and so on. A matching M for which there is no matching M^' such that M^' gets a bigger number of votes than M, when M and M^' are compared in the way described above, is then called clan-popular. Popular matchings have been studied quite extensively, especially in the one-to-one setting. In the many-to-many setting we provide a characterisation of popular and clan-popular matchings, show NP-hardness results for very restricted cases of the above problems and for certain versions describe novel polynomial algorithms. The given characterisation is also valid for popular matchings in the one-to-one setting." @default.
- W2056576409 created "2016-06-24" @default.
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- W2056576409 date "2014-08-01" @default.
- W2056576409 modified "2023-09-29" @default.
- W2056576409 title "Popular and clan-popular b -matchings" @default.
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- W2056576409 doi "https://doi.org/10.1016/j.tcs.2014.04.017" @default.
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