Diffusion-Network Alignment: An Efficient Algorithm and Explicit Probability Bounds

2026-06-12 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

A new study introduces the diffusion–network alignment problem, addressing information asymmetry where a rooted diffusion tree (e.g., from communication or contact tracing) must be aligned with a fully observed network (e.g., a social network). This problem differs from classic network alignment by not assuming full observability of both networks. Researchers propose an efficient, polynomial-time algorithm, running in n^(2+o(1)) time, which employs a two-pass procedure (upward and downward) utilizing four tree correlation test-based matching criteria. The algorithm's performance is analyzed in the sparse graph regime, demonstrating global correctness with high probability, meaning all matched pairs are accurate. Furthermore, it establishes explicit depth-dependent lower bounds on the probability of correctly matching individual vertices, with higher probabilities for vertices closer to the root. The model combines the correlated Erdős–Rényi graph pair model with an Independent Cascade diffusion process.

Key takeaway

For research scientists developing network alignment solutions, this work highlights the critical need to account for information asymmetry in real-world data. You should consider adopting the proposed polynomial-time, two-pass algorithm, which offers provable global correctness and depth-dependent matching probabilities. This approach, leveraging tree correlation tests and information propagation, provides a robust framework for scenarios where only partial network observations, like diffusion trees, are available.

Key insights

Diffusion-network alignment leverages local tree correlation tests and two-pass information propagation to match partially observed diffusion trees to full networks.

Principles

• Information asymmetry necessitates specialized alignment algorithms.
• Aggregating local neighborhood evidence improves global matching accuracy.
• Matching confidence is depth-dependent, higher near the root.

Method

The algorithm uses a two-pass (upward/downward) procedure, applying four tree correlation test-based criteria to collect and propagate local matching evidence across the diffusion tree.

In practice

• Deanonymize social network users via communication traces.
• Match epidemic contact tracing data to social networks.
• Align blockchain transaction histories to user identities.

Topics

• Diffusion-Network Alignment
• Graph Matching
• Correlated Erdős–Rényi Graphs
• Independent Cascade Model
• Tree Correlation Tests
• Sparse Graph Algorithms

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.