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 ≥ 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 ℓ ≥ 1 the problem of finding a minimum weight maximal distance-2ℓ matching and the problem of finding a minimum weight (2ℓ − 1)-independent dominating set are NP-hard to approximate in chordal graphs within a factor of c ln |V (G)|, where c 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.