The structure of stable marriage with indifference

Manlove, D.F. (2002) The structure of stable marriage with indifference. Discrete Applied Mathematics, 122(1-3), pp. 167-181. (doi: 10.1016/S0166-218X(01)00322-5)



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We consider the stable marriage problem where participants are permitted to express indifference in their preference lists (i.e., each list can be partially ordered). We prove that, in an instance where indifference takes the form of ties, the set of strongly stable matchings forms a distributive lattice. However, we show that this lattice structure may be absent if indifference is in the form of arbitrary partial orders. Also, for a given stable marriage instance with ties, we characterise strongly stable matchings in terms of perfect matchings in bipartite graphs. Finally, we briefly outline an alternative proof of the known result that, in a stable marriage instance with indifference in the form of arbitrary partial orders, the set of super-stable matchings forms a distributive lattice.

Item Type:Articles
Additional Information:Postprint provided by the author.
Keywords:Stable marriage problem; Partial order; Tie; Strong stability; Super-stability; Distributive lattice
Glasgow Author(s) Enlighten ID:Manlove, Professor David
Authors: Manlove, D.F.
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:Discrete Applied Mathematics
Copyright Holders:©2002 Elsevier Science B.V.
First Published:First published in Discrete Applied Mathematics 122(1-3):167-181
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher.

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