Computing the effective resistance in a aystem of conducting sticks

The problem of determining the effective resistance of a network of resistors is modeled as a quadratic min-cost network flow problem. Using duality theory, it can be reformulated as an unconstrained quadratic program. Based on computational comparison with standard primal methods such as the Frank-Wolfe algorithm, the unconstrained version can be solved for more efficiently by the conjugate gradient technique. Computational results are presented for five large-scale problems from physicists' studies of conducting fibers (sticks) embedded in an insulatng polymer.