Sampling random spanning arborescences in graphs with low conductance

Sampling random spanning arborescences in directed graphs is critical for applications in network analysis, optimization, and machine learning. While many state-of-the-art methods perform well on graphs with high conductance, they often fail or generalize poorly on low-conductance graphs. Inspired by Wilson’s algorithm, we propose a novel sampling approach that overcomes this limitation by using dynamic programming to compute random walk probabilities. This avoids both inefficient walk simulations and numerically unstable Laplacian determinant calculations. Our method demonstrates superior efficiency and sampling quality in simulations, and is the only one to handle low-conductance graphs effectively.