Elastic Labels: the Two-Axis Case

One of the most challenging tasks of cartographic map lettering is the optimal placement of region information on a map. We propose as an approach to this task the elastic labeling problem, in which we are given a set of elastic rectangles as labels, each associated with a point in the plane. An elastic rectangle has a specified area but its width and height may vary. The problem then is to choose the height and width of each label, and the corner of the label to place at the associated point, so that no two labels overlap.