A graphtheoretic approach to the relative placement problem

The problem of placing components on a carrier is usually divided into two steps: computation of relative positions of cells; and the final placement so that the cells do not overlap and sufficient area is provided for routing. Using circumscribed rectangles as netmodels, the two-dimensional relative placement problem is translated into two one-dimensional graph-theoretic optimization problems, each of which is a constrained minimization of weighted arc lengths in a placement graph. These optimization problems are solved independently by an exact graph-theoretic algorithm with exponential complexity in the worst case and quadratic in realistic cases. Gate arrays are used as examples.<>