  Optimal packing of objects in containers is a critical problem in various
real-life and industrial applications. This paper investigates the
two-dimensional packing of convex polygons without rotations, where only
translations are allowed. We study different settings depending on the type of
containers used, including minimizing the number of containers or the size of
the container based on an objective function.
  Building on prior research in the field, we develop polynomial-time
algorithms with improved approximation guarantees upon the best-known results
by Alt, de Berg and Knauer, as well as Aamand, Abrahamsen, Beretta and Kleist,
for problems such as Polygon Area Minimization, Polygon Perimeter Minimization,
Polygon Strip Packing, and Polygon Bin Packing. Our approach utilizes a
sequence of object transformations that allows sorting by height and
orientation, thus enhancing the effectiveness of shelf packing algorithms for
polygon packing problems. In addition, we present efficient approximation
algorithms for special cases of the Polygon Bin Packing problem, progressing
toward solving an open question concerning an O(1)-approximation algorithm for
arbitrary polygons.
