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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Elsevier
• ISSN: 0166-218X
• 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.