Popular Matchings in the Capacitated House Allocation Problem

Manlove, D.F. and Sng, C.T.S. (2006) Popular Matchings in the Capacitated House Allocation Problem. In: Proceedings of ESA 2006: the 14th Annual European Symposium on Algorithms, Zurich, Switzerland, 11-13 September 2006, pp. 492-503. ISBN 978-3-540-38875-3 (doi: 10.1007/11841036_45)

Abstract

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(√C+n₁m) 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(√Cn₁+m) algorithm for the analogous problem.

• Item Type: Conference Proceedings
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Manlove, D.F., and Sng, C.T.S.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Research Group: Formal Analysis, Theory and Algorithms
• Journal Name: Lecture Notes in Computer Science
• Publisher: Springer
• ISSN: 0302-9743
• ISBN: 978-3-540-38875-3
• Copyright Holders: Copyright © 2006 Springer
• First Published: First published in the Lecture Notes in Computer Science 4168:492-503
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher