Grid layouts of block diagrams — bounding the number of bends in each connection

Abstract

Consider an input data which specifies rectangular modules and connections between them; this is a graph. The size of the modules and the placements of the terminals on them is given as part of the input. We produce a block diagram, conforming to the input. The block diagram is on the rectilinear grid, and each edge (connection between modules) has few bends. For planar input, a linear-time algorithm is described to construct a planar drawing with at most 6 bends in each self-loop and at most 4 bends in any other edge. The external face of the drawing may be specified by the user. We show a planar input with no self-loops which has no drawing with at most 3 bends in every edge and another planar input which has no drawing with at most 5 bends in every self-loop. A linear-time algorithm is described to construct a nonplanar drawing of any input, with at most 4 bends in each edge. We show inputs that have no drawing with at most 3 bends in every edge.