Parameterized Complexity and Local Search Approaches for the Stable Marriage Problem with Ties

Authors:
Dániel Marx;Ildikó Schlotter
Affiliations:
Budapest University of Technology and Economics, Department of Computer Science and Information Theory, 1521, Budapest, Hungary;Budapest University of Technology and Economics, Department of Computer Science and Information Theory, 1521, Budapest, Hungary
Venue:
Algorithmica - Special Issue: Matching Under Preferences; Guest Editors: David F. Manlove, Robert W. Irving and Kazuo Iwama
Year:
2010

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Abstract

We consider the variant of the classical Stable Marriage problem where preference lists can be incomplete and may contain ties. In such a setting, finding a stable matching of maximum size is NP-hard. We study the parameterized complexity of this problem, where the parameter can be the number of ties, the maximum or the overall length of ties. We also investigate the applicability of a local search algorithm for the problem. Finally, we examine the possibilities for giving an FPT algorithm or an FPT approximation algorithm for finding an egalitarian or a minimum regret matching.