  In a graph $G$, a vertex subset $S\subseteq V(G)$ is said to be a dominating
set of $G$ if every vertex not in $S$ is adjacent to a vertex in $S$. A
dominating set $S$ of a graph $G$ is called a paired-dominating set if the
induced subgraph $G[S]$ contains a perfect matching. The paired-domination
problem involves finding a smallest paired-dominating set of $G$. Given an
intersection model of an interval graph $G$ with sorted endpoints, Cheng et al.
designed an $O(m+n)$-time algorithm for interval graphs and an $O(m(m+n))$-time
algorithm for circular-arc graphs. In this paper, to solve the
paired-domination problem in interval graphs, we propose an $O(n)$-time
algorithm that searches for a minimum paired-dominating set of $G$
incrementally in a greedy manner. Then, we extend the results to design an
algorithm for circular-arc graphs that also runs in $O(n)$ time.
