An improved approximation lower bound for finding almost stable maximum matchings
In the stable marriage problem that allows incomplete preference lists, all stable matchings for a given instance have the same size. However, if we ignore the stability, there can be larger matchings. Biro et al. defined the problem of finding a maximum cardinality matching that-contains minimum number of blocking pairs. They proved that this problem is not approximable within some constant delta > 1 unless P = NP, even when all preference lists are of length at most 3. In this paper, we improve this constant delta to n(1-epsilon) for any epsilon > 0, where n is the number of men in an input. (C) 2009 Elsevier B.V. All rights reserved.
the stable marriage problem approximation algorithms approximation ratio polynomial-time reduction