  Orthogonal graph drawings are used in applications such as UML diagrams, VLSI
layout, cable plans, and metro maps. We focus on drawing planar graphs and
assume that we are given an \emph{orthogonal representation} that describes the
desired shape, but not the exact coordinates of a drawing. Our aim is to
compute an orthogonal drawing on the grid that has minimum area among all grid
drawings that adhere to the given orthogonal representation.
  This problem is called orthogonal compaction (OC) and is known to be NP-hard,
even for orthogonal representations of cycles [Evans et al., 2022]. We
investigate the complexity of OC with respect to several parameters. Among
others, we show that OC is fixed-parameter tractable with respect to the most
natural of these parameters, namely, the number of \emph{kitty corners} of the
orthogonal representation: the presence of pairs of kitty corners in an
orthogonal representation makes the OC problem hard. Informally speaking, a
pair of kitty corners is a pair of reflex corners of a face that point at each
other. Accordingly, the number of kitty corners is the number of corners that
are involved in some pair of kitty corners.
