Next-Gen Graph Learning: Faster Decoding for Non-Adaptive Erdős-Rényi Models
By Hoang Ta, Jonathan Scarlett
Published on November 24, 2025| Vol. 1, Issue No. 1
Content Source
This is a curated briefing. The original article was published on cs.LG updates on arXiv.org.
Summary
This research addresses the challenge of learning unknown Erd\H{o}s--R\'enyi (ER) random graphs using non-adaptive group queries, where tests are pre-designed and report the presence of any edge within queried node subsets. While prior methods achieved an optimal number of tests, \(O(\bar{k}\log n)\), they suffered from high decoding times, often quadratic in the number of nodes (\(\Omega(n^2)\)). This paper introduces a novel scheme that extends the binary splitting approach, traditionally used in non-adaptive group testing, to ER graph learning. The proposed method not only maintains the order-optimal number of tests, but crucially, dramatically reduces the decoding time to \(O(\bar{k}^{1+\delta}\log n)\) for any fixed \(\delta>0\), enabling efficient recovery of the edge set with high probability.
Why It Matters
The ability to efficiently learn graph structures is fundamental across numerous AI domains, from understanding social networks and knowledge graphs to enhancing recommendation systems, drug discovery, and cybersecurity. This work provides a significant practical advancement by addressing a critical bottleneck in non-adaptive graph learning: decoding speed. In scenarios where tests are expensive, time-consuming, or must be planned in advance (e.g., certain biological experiments, large-scale sensor deployments, or industrial quality control), non-adaptive strategies are essential. However, if the subsequent computational decoding is too slow, the method remains impractical for large-scale, real-world datasets. This paper's achievement of simultaneously optimal test complexity and nearly optimal decoding speed makes non-adaptive learning of Erd\H{o}s--R\'enyi graphs-a common model for random network structures-far more viable. It signifies a broader trend in AI research focused on developing not just theoretically sound, but also computationally efficient, algorithms that can scale to the demands of modern data, thereby accelerating discovery and deployment in various applications reliant on complex network analysis.