The algorithm and application for the symmetrical routing

In the integrated circuit routing, we often consider the routing for some special nets under the restrictions, such as equidistance and symmetry. The symmetrical routing is operated between the routing for the bus and the clock and the routing for most the others without the priority. We prove that the symmetrical routing problem under the H-V model is equivalent to finding a Steiner tree of the corresponding vertices for all of the pins in the valid connected graph. We put forward an algorithm for the symmetrical routing under the H-V model. In the actual wiring process, when the symmetrical routing is needed, the routing is finished by hand. This paper provides a method and the theory based on graphs for the automation design of the symmetrical routing.