On enumerating all minimal solutions of feedback problems Original Research Article

We present an algorithm that generates all (inclusion-wise) minimal feedback vertex sets of a directed graph G=(V,E). The feedback vertex sets of G are generated with a polynomial delay of O(|V|2(|V|+|E|)). We further show that the underlying technique can be tailored to generate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polynomial delay of O(|V| |E| (|V|+|E|). Finally, we prove that computing the number of minimal feedback arc sets is #P-hard.