Enumerating Contingency Tables via Random Permanents

N/N !. In many cases, lnT ′ provides an asymptotically accurate estimate of lnT . The idea of the algorithm is to express T as the expectation of the permanent of an N ×N random matrix with exponentially distributed entries and approximate the expectation by the integral T ′ of an efficiently computable log-concave function on R. Applications to counting integer flows in graphs are also discussed.