On the routability of a convex grid

Abstract

We give necessary and sufficient conditions to lay out the nets of a convex grid, in the knockknee model. Convex grids, defined by Nishizeki, Saito, Suzuki [9], include the common rectilinear channel, as well as L-, T-, and X-shaped regions. Whether a convex grid can be laid out can be determined in time which is linear in the perimeter of the grid. The algorithm of [9] to accomplish this is incomplete.