  In information visualization, the position of symbols often encodes
associated data values. When visualizing data elements with both a numerical
and a categorical dimension, positioning in the categorical axis admits some
flexibility. This flexibility can be exploited to reduce symbol overlap, and
thereby increase legibility. In this paper we initialize the algorithmic study
of optimizing symbol legibility via a limited displacement of the symbols.
Specifically, we consider unit square symbols that need to be placed at
specified $y$-coordinates. We optimize the drawing order of the symbols as well
as their $x$-displacement, constrained within a rectangular container, to
maximize the minimum visible perimeter over all squares. If the container has
width and height at most $2$, there is a point that stabs all squares. In this
case, we prove that a staircase layout is arbitrarily close to optimality and
can be computed in $O(n\log n)$ time. If the width is at most $2$, there is a
vertical line that stabs all squares, and in this case, we give a
2-approximation algorithm that runs in $O(n\log n)$ time. As a minimum visible
perimeter of $2$ is always trivially achievable, we measure this approximation
with respect to the visible perimeter exceeding $2$. We show that, despite its
simplicity, the algorithm gives asymptotically optimal results for certain
instances.
