  The use of combinatorial optimization algorithms has contributed
substantially to the major progress that has occurred in recent years in the
understanding of the physics of disordered systems, such as the random-field
Ising model. While for this system exact ground states can be computed
efficiently in polynomial time, the related random-field Potts model is {\em
NP\} hard computationally. While thus exact ground states cannot be computed
for large systems in this case, approximation schemes based on graph cuts and
related techniques can be used. Here we show how a combination of such methods
with repeated runs allows for a systematic extrapolation of relevant system
properties to the ground state. The method is benchmarked on a special class of
disorder samples for which exact ground states are available.
