Routing for chip-package-board co-design considering differential pairs

Nanometer effects have complicated the designs of chips as well as packages and printed circuit boards (PCBpsilas). In order to improve the performance, convergence, and signal integrity of the design, chip-package-board co-design is strongly recommended by industry. In this paper, we present the first routing algorithm in the literature for chip-package-board co-design with differential-pair considerations. Our algorithm is based on linear programming and integer linear programming and guarantees to find an optimal solution for the addressed problem. It first creates global-routing paths among chips, packages, and a PCB. Without loss of the solution optimality, our routing formulation can reduce the numbers of integer variables (constraints) by 95% (99%) on average. Then, any-angle routing is applied to complete the routing. Experimental results based on five real industry designs show that our router can achieve 100% routability and the optimal global-routing wirelength and satisfy all differential-pair constraints, under reasonable CPU times, whereas recent related work results in much inferior solution quality.