Computing at Glasgow University
Paper ID: 6769
DCS Tech Report Number: TR-2002-123

Strong Stability in the Hospitals/Residents Problem
Irving,R.W. Manlove,D.F. Scott,S.

Publication Type: Tech Report (internal)
Appeared in: DCS Tech Report
Page Numbers :
Publisher: Dept of Computing Science, University of Glasgow
Year: 2002

Note: Revised May 2005


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.

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