In various models of matching markets, substitutable preferences constitute the largest domain for which stable matchings are guaranteed to exist. Recently, Hatfield et al. (2012) have proposed an efficient algorithm to test substitutability of strict preferences. In this note we show how the...

We present the first polynomial-time algorithm for computing the minimal covering set of a (weak) tournament. The algorithm draws upon a linear programming formulation of a subset of the minimal covering set known as the essential set. On the other hand, we show that no efficient algorithm...