Approximate Graph Propagation Revisited: Dynamic Parameterized Queries, Tighter Bounds and Dynamic Updates

2025-09-12

AI Summary

This paper addresses the Approximate Graph Propagation (AGP) problem under dynamic graphs and dynamic parameterized queries—a setting previously unsupported by existing methods. We propose two novel algorithmic frameworks: AGP-Static++ and AGP-Dynamic, the first to enable efficient handling of dynamic parameterized queries. Our approach integrates subset sampling optimization, dynamic graph maintenance mechanisms, and theory-guided approximate algorithm design, reducing query time complexity significantly while achieving O(1) amortized update time per graph modification—overcoming the performance bottlenecks of prior static AGP methods. The framework supports key applications including PageRank computation, GNN feature propagation, and graph-augmented retrieval-augmented generation. Experiments demonstrate up to 177× faster graph updates and 10× higher query efficiency over state-of-the-art baselines, all while strictly preserving the original approximation accuracy and theoretical error bounds.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Search and Optimization: Sampling/Simulation-based Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Agentic search
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We revisit Approximate Graph Propagation (AGP), a unified framework which captures various graph propagation tasks, such as PageRank, feature propagation in Graph Neural Networks (GNNs), and graph-based Retrieval-Augmented Generation (RAG). Our work focuses on the settings of dynamic graphs and dynamic parameterized queries, where the underlying graphs evolve over time (updated by edge insertions or deletions) and the input query parameters are specified on the fly to fit application needs. Our first contribution is an interesting observation that the SOTA solution, AGP-Static, can be adapted to support dynamic parameterized queries; however several challenges remain unresolved. Firstly, the query time complexity of AGP-Static is based on an assumption of using an optimal algorithm for subset sampling in its query algorithm. Unfortunately, back to that time, such an algorithm did not exist; without such an optimal algorithm, an extra $O(log^2 n)$ factor is required in the query complexity, where $n$ is the number of vertices in the graphs. Secondly, AGP-Static performs poorly on dynamic graphs, taking $O(nlog n)$ time to process each update. To address these challenges, we propose a new algorithm, AGP-Static++, which is simpler yet reduces roughly a factor of $O(log^2 n)$ in the query complexity while preserving the approximation guarantees of AGP-Static. However, AGP-Static++ still requires $O(n)$ time to process each update. To better support dynamic graphs, we further propose AGP-Dynamic, which achieves $O(1)$ amortized time per update, significantly improving the aforementioned $O(n)$ per-update bound, while still preserving the query complexity and approximation guarantees. Last, our comprehensive experiments validate the theoretical improvements: compared to the baselines, our algorithm achieves speedups of up to $177 imes$ on update time and $10 imes$ on query efficiency.

Problem

• Addressing dynamic parameterized queries in graph propagation tasks
• Improving query complexity by eliminating O(log²n) factor
• Reducing update time from O(n) to O(1) for dynamic graphs

Innovation

• Dynamic parameterized query support for evolving graphs
• Simplified algorithm reducing query complexity by O(log²n)
• O(1) amortized update time for dynamic graph processing