A polynomial time algorithm for optimal routing around a rectangle

In this paper we present an algorithm for a special case of wire routing. Given a rectangular circuit component on a planar surface with terminals around its boundary, the algorithm finds an optimal set of paths in the plane connecting specified pairs of terminals. The paths are restricted to lie on the outside of the component and must consist of line segments orthogonal to the sides of the component. Paths may intersect at a point but may not overlap. The criterion for optimality is the area of a rectangle with sides orthogonal to those of the component which circumscribes the component and paths. The algorithm has running time O(t3), where t is the number of terminals on the component.