Strong stability in the Hospitals/Residents problem

Irving, R.W., Manlove, D.F. and Scott, S. (2003) Strong stability in the Hospitals/Residents problem. In: Proceedings of STACS 2003: the 20th International Symposium on Theoretical Aspects of Computer Science, Berlin, Germany, 27 February - 1 March, 2003, pp. 439-450. ISBN 3-540-00623-0

Abstract

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(a^2) 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.

• Item Type: Conference Proceedings
• Keywords: stable matching problem; strong stability; hospitals / residents problem; polynomial-time algorithm; lower bound; NP-completeness
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Irving, R.W., Manlove, D.F., and Scott, S.
• 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
• Publisher: Springer-Verlag GmbH
• ISSN: 0302-9743
• ISBN: 3-540-00623-0
• Copyright Holders: © Springer
• First Published: First published in Lecture Notes in Computer Science 2607:439-450
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.