Flipping modules to improve circuit performance and routability

Preplaced modules may be flipped to improve performance and/or routability. We show that several versions of the module flipping problem are NP-hard. We propose algorithms to obtain module orientations that minimize the total wire length for module matrix and standard cell models. Additionally, we propose a heuristic to flip modules so as to minimize the length of the longest signal path. The results of experiments performed with this heuristic are also presented