Bernoulli Factories for Flow-Based Polytopes

TL;DR

This paper develops explicit Bernoulli factories for flow-based polytopes, enabling exact sampling of network flows and revealing new links to algebraic combinatorics.

Contribution

It generalizes previous work by constructing Bernoulli factories for a broad class of flow polytopes, facilitating exact sampling methods.

Findings

Constructed explicit Bernoulli factories for flow-based polytopes

Provided novel sampling procedures for paths, circulations, and k-flows

Uncovered new connections to algebraic combinatorics

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.