<XML><RECORDS><RECORD><REFERENCE_TYPE>10</REFERENCE_TYPE><REFNUM>7098</REFNUM><AUTHORS><AUTHOR>Cechlarova,K.</AUTHOR><AUTHOR>Manlove,D.F.</AUTHOR></AUTHORS><YEAR>2003</YEAR><TITLE>The Exchange-Stable Marriage Problem</TITLE><PLACE_PUBLISHED>DCS Tech Report</PLACE_PUBLISHED><PUBLISHER>Dept of Computing Science, University of Glasgow</PUBLISHER><ISBN>TR-2003-142</ISBN><LABEL>Cechlarova:2003:7098</LABEL><KEYWORDS><KEYWORD>Stable Marriage problem; Exchange-stable matching; Man-exchange-stable matching; NP-completeness; Polynomial-time algorithm</KEYWORD></KEYWORDS<ABSTRACT>In this paper we consider instances of stable matching problems, namely the classical Stable Marriage (SM) and Stable Roommates (SR) problems and their variants. In such instances we consider a stability criterion that has recently been proposed, that of exchange-stability. In particular, we prove that ESM - the problem of deciding, given an SM instance, whether an exchange-stable matching exists - is NP-complete. This result is in marked constrast with Gale and Shapley's classical linear-time algorithm for finding a stable matching in an instance of SM. We also extend the result for ESM to the SR case. Finally, we study some variants of ESM under a weaker form of exchange-stability, presenting both polynomial-time solvability and NP-completeness results for the corresponding existence questions.</ABSTRACT></RECORD></RECORDS></XML>