Approximation Algorithms for Maximum Stable Matching with Matroids and Partial Orders

There exists a simple 1.5-approximation algorithm for finding a maximum stable matching in the matroid kernel problem when the preferences are given as interval orders, a broad subclass of partial orders. However, for general partial orders, it is NP-hard to approximate the maximum stable marriage problem within a factor better than 2 assuming the Unique Games Conjecture.