Computing Grounded Extensions Of Abstract Argumentation Frameworks

An abstract argumentation framework is a directed graph (V, E) such that the vertices of V denote abstract arguments and E subset of V x V represents the attack relation between them. We present a new ad hoc algorithm for computing the grounded extension of an abstract argumentation framework. We show that the new algorithm runs in O(vertical bar V vertical bar + vertical bar E vertical bar) time. In contrast, the existing state-of-the-art algorithm runs in O(vertical bar V vertical bar vertical bar S vertical bar vertical bar E vertical bar) time where S is the grounded extension of the input graph.