## Abstract

A well-known and well-investigated family of hard optimization problems concerns variants of the cutting
stock or nesting problem, i.e. the non-overlapping
placing of polygons to be cut from a rectangle or the
plane whilst minimizing the waste. Here we consider
an in some sense inverse problem. Concretly, given
a set of polygons in the plane, we seek the minimum
number of rectangles of a given shape such that every
polygon is covered by at least one rectangle. As motions of the given rectangle we investigate the cases
of translation and of translation combined with rotation.