Abstract
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.
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