Optimal cooperation and submodularity for computing Potts' partition functions with a large number of states

The partition function of the q-state Potts model with random ferromagnetic couplings in the large-q limit is generally dominated by the contribution of a single diagram of the high temperature expansion. Computing this dominant diagram amounts to minimizing a particular submodular function. We provide a combinatorial optimization algorithm, the optimal cooperation algorithm, which works in polynomial time for any lattice. The implementation of the method and its running time are also discussed.