Ball Grid Array packages in which I/O pins are arranged in a grid array pattern realize a number of connections between chips and PCB, but it takes much time in manual routing. So the demand for automation of package routing is increasing. In this paper, we give the necessary and sufficient condition that all nets can be connected by monotonic routes when a net consists of a finger and a ball and fingers are on the two parr allel boundaries of the Ball Grid Array package, and propose a monotonic routing method based on this condition. Moreover, we give a necessary condition and a sufficient condition when fingers are on the two orthogonal boundaries, and propose a monotonic routing method based on the necessary condition.
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