Note: Blockers and antiblockers of stable matchings

Authors:
Pavlos Eirinakis;Dimitrios Magos;Ioannis Mourtos
Affiliations:
Department of Management Science and Technology, Athens University of Economics and Business, 76 Patission Ave., 104 34 Athens, Greece;Department of Informatics, Technological Educational Institute of Athens, Ag. Spyridonos Str., 12210 Egaleo, Greece;Department of Management Science and Technology, Athens University of Economics and Business, 76 Patission Ave., 104 34 Athens, Greece
Venue:
Theoretical Computer Science
Year:
2014

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Abstract

An implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid-kernel polytope. The explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates. Here, we expose the relation of such a partition to rotations. We provide a time-optimal algorithm for obtaining such a partition and establish some new related results; most importantly, that this partition is unique.