  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 do would have implied an
exponential complexity), our best performing algorithm yields results that are
only marginally bigger. 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.
