Ollivier-Ricci curvature is a powerful tool for analyzing graph structure, but it comes at a steep computational price: evaluating it on large graphs requires solving an optimal transport problem for every edge. That makes many practical applications infeasible as graph size grows.
A new preprint on arXiv (2603.13535) tackles this bottleneck directly. Instead of computing exact Ollivier-Ricci curvature, the authors derive explicit, two-sided edgewise envelopes that relate balanced Forman curvature to Ollivier-Ricci curvature. These envelopes provide rigorous bounds without the need for per-edge optimal transport solves.
The result is a practical path to approximating Ollivier-Ricci curvature on large-scale graphs while retaining theoretical guarantees. The abstract does not include experimental results or implementation details, so the practical speedup is not quantified here, but the mathematical approach appears to address the core computational obstacle.