New for: D3
Tree-maps are first mentioned by Shneiderman, who gives a simple slice-and-dice algorithm to compute a tree-map. However, the aspect ratio - measuring if a rectangle is close to square - can be very poor in this method. Heuristic-based methods have been developed to overcome this issue, but without guarantees on the maximal aspect ratio.
We look into aspect ratio optimization in trees of height one - consisting of a root and a number of leaves. We try to prove NP-hardness of the general problem and give solutions to guarantee a constant aspect ratio for the special cases that all leaf weights are in a certain range and that shapes other than rectangles are allowed.