Packing convex polygons into rectangular boxes

We consider the problem of packing several convex polygons into minimum size rectangles. For this purpose the polygons may be moved either by translations only, or by combinations of translations and rotations. We investigate both cases, that the polygons may overlap when being packed or that they must be disjoint. The size of a rectangle to be minimized can either be its area or its perimeter. In the case of overlapping packing very efficient algorithms whose runtime is close to linear or O(n log n) can be found even for an arbitrary number of polygons. Disjoint optimal packing is known to be NP-hard for arbitrary numbers of polygons. Here, efficient algorithms are given for disjoint packing of two polygons with a runtime close to linear for translations and O(n(3)) for general isometries.