A Faster Practical Approximation Scheme for the Permanent

The permanent of a matrix has numerous applications but is notoriously hard to compute. While nonnegative matrices admit polynomial approximation schemes based on rapidly mixing Markov chains, the known practical estimators rely importance or rejection sampling. We advance sampling approach, which provides probabilistic accuracy guarantees, unlike Specifically, we give novel class nesting upper bounds and simple preprocessing method that, in comparison previous works, enable faster with better acceptance rate; demonstrate order-of-magnitude improvements both theoretical empirical analyses. In addition, display instances our scheme competitive against state-of-the-art estimators.