Bernoulli Factories for Flow-Based Polytopes

Abstract: We construct explicit combinatorial Bernoulli factories for the class of \emph{flow-based polytopes}; integral 0/1-polytopes defined by a set of network flow constraints. This generalizes the results of Niazadeh et al. (who constructed an explicit factory for the specific case of bipartite perfect matchings) and provides novel exact sampling procedures for sampling paths, circulations, and $k$-flows. In the process, we uncover new connections to algebraic combinatorics.