Algorithms for the qualitative analysis of nonlinear resistive circuits

An algorithm that decides whether a given resistive circuit has a pair of conjugate trees and/or a nontrivial uniform partial orientation of the resistors is presented. The algorithm in the case of conjugate trees is of polynomial order in the number of branches, whereas for the uniform partial orientation problem it is potentially of exponential complexity. However, the constraint-propagation method is capable of reducing considerably the computational burden for the orientation problem. The two problems are central to the qualitative analysis of nonreciprocal circuits