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.