Paper ID: 9317
Popular Matchings in the Weighted Capacitated House Allocation Problem
Sng,C.T.S.
Manlove,D.F.
Publication Type:
Journal
Appeared in:
Journal of Discrete Algorithms, volume 8
Page Numbers : 102116
Publisher: Elsevier Science
Year: 2010
ISBN/ISSN:
URL: This publication is available at this URL.
Abstract:
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 be matched
to it. A matching M of agents to houses is popular if there
is no other matching M' such that the total weight of the
agents who prefer their allocation in M' to that in M
exceeds the total weight of the agents who prefer their
allocation in M to that in M'. Here, we give an
O(\sqrt{C}n1+m) algorithm to determine if an instance of
WCHA 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.
Keywords: Popular matching problem; Priorities; Strict preference lists; Maximum popular matching; Polynomialtime algorithm
