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Journal of Combinatorial Optimization

, Volume 16, Issue 3, pp 279–292 | Cite as

Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems

  • Robert W. IrvingEmail author
  • David F. Manlove
Article

Abstract

When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes.

Keywords

Stable matching Weak stability NP-hard problems Approximation algorithms 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowUK

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