  Subtraction-free computational complexity is the version of arithmetic
circuit complexity that allows only three operations: addition, multiplication,
and division.
  We use cluster transformations to design efficient subtraction-free
algorithms for computing Schur functions and their skew, double, and
supersymmetric analogues, thereby generalizing earlier results by P. Koev.
  We develop such algorithms for computing generating functions of spanning
trees, both directed and undirected. A comparison to the lower bound due to M.
Jerrum and M. Snir shows that in subtraction-free computations, "division can
be exponentially powerful."
  Finally, we give a simple example where the gap between ordinary and
subtraction-free complexity is exponential.
