Computing Grounded Extensions Of Abstract Argumentation Frameworks

Abstract An abstract argumentation framework is a directed graph $(V,E)$ such that the vertices of $V$ denote abstract arguments and $E \subseteq V \times V$ 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 $\mathcal{O}(|V|+|E|)$ time. In contrast, the existing state-of-the-art algorithm runs in $\mathcal{O}(|V|+|S||E|)$ time where $S$ is the grounded extension of the input graph.