Abstract

When ties and incomplete preference lists are permitted in the Stable Marriage problem, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe a polynomial-time \(\frac{8}{5}\)-approximation algorithm for a variant in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralized matching schemes.

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