Tractable Algorithms for Strong Admissibility

Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept
underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded
extension. As such, strongly admissible sets and labellings can be used as an explanation of membership of the grounded
extension, as is for instance done in some of the proof procedures for grounded semantics. In the current paper, we present two
polynomial algorithms for constructing relatively small strongly admissible labellings, with associated min-max numberings,
for a particular argument. These labellings can be used as relatively small explanations for the argument’s membership of the
grounded extension. Although our algorithms are not guaranteed to yield an absolute minimal strongly admissible labelling for
the argument (as doing so would have implied an exponential complexity), our best performing algorithm yields results that
are only marginally larger. Moreover, the runtime of this algorithm is an order of magnitude smaller than that of the existing
approach for computing an absolute minimal strongly admissible labelling for a particular argument. As such, we believe
that our algorithms can be of practical value in situations where the aim is to construct a minimal or near-minimal strongly
admissible labelling in a time-efficient way.