An algorithm for the via assignment problem in multilayer backboard wiring

The multilayer routing approach first introduced by So is one of the most promising to the layout especially for large-scale multilayer backboards. Associated with this, the problem of which vias are to be assigned for each signal net is an important factor to reduce the number of via columns, and hence the wiring area of a backboard. In this paper, we first formulate an optimization portion of this problem and consider its inherent computational complexity to reveal that this problem belongs to the
P
-complete class. We then propose a heuristic polynomial-time algorithm to this problem.