  Given a graph $G=(V,E)$ and an integer $k \ge 1$, a $k$-hop dominating set
$D$ of $G$ is a subset of $V$, such that, for every vertex $v \in V$, there
exists a node $u \in D$ whose hop-distance from $v$ is at most $k$. A $k$-hop
dominating set of minimum cardinality is called a minimum $k$-hop dominating
set. In this paper, we present linear-time algorithms that find a minimum
$k$-hop dominating set in unicyclic and cactus graphs. To achieve this, we show
that the $k$-dominating set problem on unicycle graph reduces to the piercing
circular arcs problem, and show a linear-time algorithm for piercing sorted
circular arcs, which improves the best known $O(n\log n)$-time algorithm.
