  We study the computational complexity of several problems connected with
finding a maximal distance-$k$ matching of minimum cardinality or minimum
weight in a given graph. We introduce the class of $k$-equimatchable graphs
which is an edge analogue of $k$-equipackable graphs. We prove that the
recognition of $k$-equimatchable graphs is co-NP-complete for any fixed $k \ge
2$. We provide a simple characterization for the class of strongly chordal
graphs with equal $k$-packing and $k$-domination numbers. We also prove that
for any fixed integer $\ell \ge 1$ the problem of finding a minimum weight
maximal distance-$2\ell$ matching and the problem of finding a minimum weight
$(2 \ell - 1)$-independent dominating set cannot be approximated in polynomial
time in chordal graphs within a factor of $\delta \ln |V(G)|$ unless
$\mathrm{P} = \mathrm{NP}$, where $\delta$ is a fixed constant (thereby
improving the NP-hardness result of Chang for the independent domination case).
Finally, we show the NP-hardness of the minimum maximal induced matching and
independent dominating set problems in large-girth planar graphs.
