  Combinatorial optimization algorithms which compute exact ground state
configurations in disordered magnets are seen to exhibit critical slowing down
at zero temperature phase transitions. Using arguments based on the physical
picture of the model, including vanishing stiffness on scales beyond the
correlation length and the ground state degeneracy, the number of operations
carried out by one such algorithm, the push-relabel algorithm for the random
field Ising model, can be estimated. Some scaling can also be predicted for the
2D spin glass.
