Network flow based BSM asssignment

in current industry practice, Bottom Surface Metals (BSMs) assignment for high frequency signals on a package device is a tedious manual job. One often needs to change the assignment multiple times in order to produce a routable solution. This paper proposes a network flow based method to assign BSMs automatically. It constructs a network flow graph based on available routing resource, honoring constraints such as wiring/BSM blockages. Then it derives the BSM assignment from the min-cost max-flow solution. The resulting assignment is optimal in terms of routability and wirelength. In practice, some high speed signals require differential pair routing. This paper proposes a two-step BSM assignment algorithm to handle these differential pair constraints. The first step constructs a bi-partite graph which solves the BSM pairing problem automatically. The second step constructs a scaled flow graph to assign BSM pairs to differential pairs. Compared to the manual approach, these methods can provide an optimized solution which also significantly reduces the turn around time of board design process from days to seconds.