Ordered Escape routing for grid pin array based on Min-cost Multi-commodity Flow

Ordered Escape routing is a critical issue in high-speed PCB routing. In this paper, for the first time, a Min-cost Multi-commodity Flow (MMCF) approach is proposed to solve the ordered escape routing. The characteristic of grid pin array is analyzed and then a basic network model is used to convert ordered escape routing to MMCF model. To satisfy the constraints of ordered escape routing, three novel transformations, such as non-crossing transformation, ordering transformation and capacity transformation, are used to convert the basic network model to the final correct MMCF model. Experimental results show that our method achieves 100% routability for all the test cases. The method can get both a feasible solution and an optimal solution. Compared to published approaches, our method improves in both wire length and CPU time remarkably.