An approximation algorithm for the via placement problem

The authors consider the via placement problem that arises in multilayer printed circuit board (MPCB) layout systems. It is shown that this problem can be formulated as an integer linear max-flow problem. Since the integer linear max-flow problem is an NP-complete problem, it is unlikely that one can find an efficient algorithm for its solution. However, a solution to this via placement problem can be obtained by relaxing the integer constraints in the integer linear max-flow problem. A solution to the relaxed linear max-flow problem can be obtained by solving a linear programming problem. The procedure generates in time bounded by a low order polynomial a placement with no more than 2× d_OPT density, where D_OPT is the density in an optimal placement