A slicing floorplan is a decomposition of a rectangle with horizontal and vertical sides using horizontal and vertical cuts $($see Figure $7\mathrm{.}24($a$)).$ A slicing floorplan can be represented by a binary tree, called a slicing tree, whose internal nodes represent the cuts, and whose external nodes repre$-$ sent the basic rectangles into which the floorplan is decomposed by the cuts $($see Figure $7\mathrm{.}24($b$)).$ The compaction problem is defined as follows. Assume that each basic rectangle of a slicing floorplan is assigned a minimum width w and a minimum height h$.$ The compaction problem is to find the smallest possible height and width for each rectangle of the slicing floorplan that is compatible with the minimum dimensions of the basic rectangles. Namely, this problem requires the assignment of values h$($v$)$ and w$($v$)$ to each node v of the slicing tree, such that