A Residual-Shell-Based Lower Bound for Ollivier-Ricci Curvature
This work addresses the computational bottleneck of Ollivier-Ricci curvature for graph analysis, enabling its broader use in network science and machine learning.
The authors propose a new lower bound for Ollivier-Ricci curvature that is significantly tighter than existing bounds while being tens of times faster to compute than exact curvature, applicable to k-hop random walks.
Ollivier-Ricci curvature (ORC), defined via the Wasserstein distance that captures rich geometric information, has received growing attention in both theory and applications. However, the high computational cost of Wasserstein distance evaluation has significantly limited the broader practical use of ORC. To alleviate this issue, previous work introduced a computationally efficient lower bound as a proxy for ORC based on 1-hop random walks, but this approach empirically exhibits large gaps from the exact ORC. In this paper, we establish a substantially tighter lower bound for ORC than the existing lower bound, while retaining much lower computational cost than exact ORC computation, with practical speedups of tens of times. Moreover, our bound is not restricted to 1-hop random walks, but also applies to k-hop random walks (k > 1). Experiments on several fundamental graph structures demonstrate the effectiveness of our bound in terms of both approximation accuracy and computational efficiency.