Keeping partners together: algorithmic results for the hospitals/residents problem with couples

Eric J. McDermid () and David F. Manlove ()
Additional contact information
Eric J. McDermid: University of Glasgow
David F. Manlove: University of Glasgow

Journal of Combinatorial Optimization, 2010, vol. 19, issue 3, No 3, 279-303

Abstract: Abstract The Hospitals/Residents problem with Couples (HRC) is a generalisation of the classical Hospitals/Residents problem (HR) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of hospitals (h i ,h j ). We consider a natural restriction of HRC in which the members of a couple have individual preference lists over hospitals, and the joint preference list of the couple is consistent with these individual lists in a precise sense. We give an appropriate stability definition and show that, in this context, the problem of deciding whether a stable matching exists is NP-complete, even if each resident’s preference list has length at most 3 and each hospital has capacity at most 2. However, with respect to classical (Gale-Shapley) stability, we give a linear-time algorithm to find a stable matching or report that none exists, regardless of the preference list lengths or the hospital capacities. Finally, for an alternative formulation of our restriction of HRC, which we call the Hospitals/Residents problem with Sizes (HRS), we give a linear-time algorithm that always finds a stable matching for the case that hospital preference lists are of length at most 2, and where hospital capacities can be arbitrary.

Keywords: Stable matching problem; NP-completeness; Polynomial-time algorithm (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (12)

Downloads: (external link)
http://link.springer.com/10.1007/s10878-009-9257-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:19:y:2010:i:3:d:10.1007_s10878-009-9257-2

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-009-9257-2

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().