Re. Bryant et al., GEOMETRIC CHARACTERIZATION OF SERIES-PARALLEL VARIABLE RESISTOR NETWORKS, IEEE transactions on circuits and systems. 1, Fundamental theory andapplications, 41(11), 1994, pp. 686-698
The range of operating conditions for a series-parallel network of var
iable linear resistors, voltage sources, and current sources can be re
presented as a convex polygon in a Thevenin or Norton half-plane. For
a network with n elements of which k are variable, these polygons have
at most 2k vertices and can be computed in O(nk) time. These half pla
nes are embedded in the real projective plane to represent circuits wi
th potentially infinite Thevenin resistance or Norton conductance. For
circuits that have an acyclic structure once all branches to ground a
re removed, the characteristics polygons for all nodes with respect to
ground can be computed simultaneously by an algorithm of complexity O
(nk).