Computing at Glasgow University
Paper ID: 6976

Strong stability in the hospitals/residents problem
Irving,R.W. Manlove,D.F. Scott,S.

Publication Type: Conference Proceedings
Appeared in: Proceedings of STACS 2003: The 20th Annual Symposium on Theoretical Aspects of Computer Science, volume 2607 of Lecture Notes in Computer Science
Page Numbers : 439-450
Publisher: Springer Verlag
Year: 2003
ISBN/ISSN: 0302-9743

URL: This publication is available at this URL.


We study a version of the well-known Hospitals/Residents problem in which participants’ preferences may involve ties or other forms of indifference. In this context, we investigate the concept of strong stability, arguing that this may be the most appropriate and desirable form of stability in many practical situations. When the indifference is in the form of ties, we describe an O(a2) algorithm to find a strongly stable matching, if one exists, where a is the number of mutually acceptable resident-hospital pairs. We also show a lower bound in this case in terms of the complexity of determining whether a bipartite graph contains a perfect matching. By way of contrast, we prove that it becomes NP-complete to determine whether a strongly stable matching exists if the preferences are allowed to be arbitrary partial orders.

Keywords: stable matching problem; strong stability; hospitals/residents problem; polynomial-time algorithm; lower bound; NP-completeness.

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