Would it be feasible to program a computer to search for solutions to the following diagramming problem, say for up to $100$ rectangles?
Given a strict partial order on $n$ rectangles of fixed areas and variable dimensions, produce a Hasse diagram (within a reasonably-sized universe rectangle of fixed dimensions) subject to the following constraints:
(1) Every edge consists of one line segment whose endpoints lie on the perimeters of the rectangles it connects.
(2) Rectangle interiors do not intersect any edges or other rectangles and the only intersections allowed on perimeters are those described above.
(3) The rectangles are all parallel to the axes and precedence is compatible with bottom-side height.
Note that edges are allowed to intersect.