On testing substitutability

The papers [1] and [2] propose algorithms for testing whether the choice function induced by a (strict) preference list of length N over a universe U is substitutable. The running time of these algorithms is O(|U|3⋅N3), respectively O(|U|2⋅N3). In this note we present an algorithm with running time O(|U|2⋅N2). Note that N may be exponenti...More