On minimal-displacement overlap removal

In the context of visualizing spatial data using proportional symbols, the following problem often arises: given a set of overlapping squares of varying sizes, reposition the squares as to remove the overlap while minimizing the displacement of the squares, constrained to maintain the orthogonal order. Though this problem is NP-hard, we show that rotating the squares by 45 degrees into diamonds allows for a linear or convex quadratic program and is thus efficiently solvable even for relatively large instances.