  We consider combinatorial optimization problems defined over random
ensembles, and study how solution cost increases when the optimal solution
undergoes a small perturbation delta. For the minimum spanning tree, the
increase in cost scales as delta^2; for the mean-field and Euclidean minimum
matching and traveling salesman problems in dimension d>=2, the increase scales
as delta^3; this is observed in Monte Carlo simulations in d=2,3,4 and in
theoretical analysis of a mean-field model. We speculate that the scaling
exponent could serve to classify combinatorial optimization problems into a
small number of distinct categories, similar to universality classes in
statistical physics.
