  We propose faster algorithms for the following three optimization problems on
$n$ collinear points, i.e., points in dimension one. The first two problems are
known to be NP-hard in higher dimensions.
  1- Maximizing total area of disjoint disks: In this problem the goal is to
maximize the total area of nonoverlapping disks centered at the points.
Acharyya, De, and Nandy (2017) presented an $O(n^2)$-time algorithm for this
problem. We present an optimal $\Theta(n)$-time algorithm.
  2- Minimizing sum of the radii of client-server coverage: The $n$ points are
partitioned into two sets, namely clients and servers. The goal is to minimize
the sum of the radii of disks centered at servers such that every client is in
some disk, i.e., in the coverage range of some server. Lev-Tov and Peleg (2005)
presented an $O(n^3)$-time algorithm for this problem. We present an
$O(n^2)$-time algorithm, thereby improving the running time by a factor of
$\Theta(n)$.
  3- Minimizing total area of point-interval coverage: The $n$ input points
belong to an interval $I$. The goal is to find a set of $n$ disks of minimum
total area, covering $I$, such that every disk contains at least one input
point. We present an algorithm that solves this problem in $O(n^2)$ time.
