The Hospitals/Residents Problem with Ties

The hospitals/residents problem is an extensively-studied many-one stable matching problem. Here, we consider the hospitals/ residents problem where ties are allowed in the preference lists. In this extended setting, a number of natural definitions for a stable matching arise. We present the first linear-time algorithm for the problem under the strongest of these criteria, so-called super-stability. Our new results have applications to large-scale matching schemes, such as the National Resident Matching Program in the US, and similar schemes elsewhere.

[1]  Robert W. Irving.  Stable Marriage and Indifference , 1994, Discret. Appl. Math..

[2]  David Manlove,et al.  Hard variants of stable marriage , 2002, Theor. Comput. Sci..

[3]  Donald E. Knuth,et al.  Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms , 1996 .

[4]  David Gale,et al.  Some remarks on the stable matching problem , 1985, Discret. Appl. Math..

[5]  A. Roth.  On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets , 1986 .

[6]  David F. Manlove,et al.  Stable Marriage with Ties and Unacceptable Partners , 1999 .

[7]  David Manlove,et al.  Stable Marriage with Incomplete Lists and Ties , 1999, ICALP.

[8]  Daniel S. Hirschberg,et al.  Lower Bounds for the Stable Marriage Problem and its Variants , 1990, SIAM J. Comput..

[9]  Robert W. Irving.  Matching Medical Students to Pairs of Hospitals: A New Variation on a Well-Known Theme , 1998, ESA.

[10]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[11]  A. Roth.  The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.

[12]  Robert W. Irving.  Matching medical students to pairs of hospitals: a new variation on an old theme , 1998 .

[13]  Robert W. Irving,et al.  The Stable marriage problem - structure and algorithms , 1989, Foundations of computing series.