Popular Matchings in the Capacitated House Allocation Problem
نویسندگان
چکیده
We consider the problem of finding a popular matching in the Capacitated House Allocation problem (CHA). An instance of CHA involves a set of agents and a set of houses. Each agent has a preference list in which a subset of houses are ranked in strict order, and each house may be matched to a number of agents that must not exceed its capacity. A matching M is popular if there is no other matching M ′ such that the number of agents who prefer their allocation in M ′ to that in M exceeds the number of agents who prefer their allocation in M to that in M ′. Here, we give an O( √ Cn1 + m) algorithm to determine if an instance of CHA admits a popular matching, and if so, to find a largest such matching, where C is the total capacity of the houses, n1 is the number of agents and m is the total length of the agents’ preference lists. For the case where preference lists may contain ties, we give an O(( √ C + n1)m) algorithm for the analogous problem.
منابع مشابه
Popular matchings in the weighted capacitated house allocation problem
We consider the problem of finding a popular matching in the Weighted Capacitated House Allocation problem (WCHA). An instance of WCHA involves a set of agents and a set of houses. Each agent has a positive weight indicating his priority, and a preference list in which a subset of houses are ranked in strict order. Each house has a capacity that indicates the maximum number of agents who could ...
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