  We discuss the computational complexity of solving linear programming
problems by means of an analog computer. The latter is modeled by a dynamical
system which converges to the optimal vertex solution. We analyze various
probability ensembles of linear programming problems. For each one of these we
obtain numerically the probability distribution functions of certain quantities
which measure the complexity. Remarkably, in the asymptotic limit of very large
problems, each of these probability distribution functions reduces to a
universal scaling function, depending on a single scaling variable and
independent of the details of its parent probability ensemble. These functions
are reminiscent of the scaling functions familiar in the theory of phase
transitions. The results reported here extend analytical and numerical results
obtained recently for the Gaussian ensemble.
