  We consider n robots with limited visibility: each robot can observe other
robots only up to a constant distance denoted as the viewing range. The robots
operate in discrete rounds that are either fully synchronous (FSync) or
semi-synchronized (SSync). Most previously studied formation problems in this
setting seek to bring the robots closer together (e.g., Gathering or
Chain-Formation). In this work, we introduce the Max-Line-Formation problem,
which has a contrary goal: to arrange the robots on a straight line of maximal
length. First, we prove that the problem is impossible to solve by robots with
a constant sized circular viewing range. The impossibility holds under
comparably strong assumptions: robots that agree on both axes of their local
coordinate systems in FSync. On the positive side, we show that the problem is
solvable by robots with a constant square viewing range, i.e., the robots can
observe other robots that lie within a constant-sized square centered at their
position. In this case, the robots need to agree on only one axis of their
local coordinate systems. We derive two algorithms: the first algorithm
considers oblivious robots and converges to the optimal configuration in time
$\mathcal{O}(n^2 \cdot \log (n/\varepsilon))$ under the SSync scheduler. The
other algorithm makes use of locally visible lights (LUMI). It is designed for
the FSync scheduler and can solve the problem exactly in optimal time
$\Theta(n)$. Afterward, we show that both the algorithmic and the analysis
techniques can also be applied to the Gathering and Chain-Formation problem: we
introduce an algorithm with a reduced viewing range for Gathering and give new
and improved runtime bounds for the Chain-Formation problem.
