Scalable Graph Coreset Selection via Greedy Sampling

2026-07-29

AI Summary

This work addresses the scalability limitations of existing graph sampling methods, which typically rely on the full graph Laplacian matrix and thus struggle with large-scale graphs. The authors propose a novel column selection algorithm based on a greedy minimum inner product criterion that, at each iteration, accesses only a small random subset of the Laplacian matrix—eliminating the need for eigendecomposition or global traversal. This approach enables scalable coreset sampling without ever storing the complete Laplacian. Theoretical analysis grounded in the stochastic block model and Paley–Wiener space demonstrates that the sampling rate aligns with cluster sizes. Empirical results on both synthetic and real-world graphs confirm the method’s effectiveness, showing that estimation error for bandlimited graph signals decreases as inter-cluster connectivity weakens.

Abstract

Sampling representative nodes from large graphs is fundamental to graph signal processing and network analysis, yet existing methods require access to the full graph Laplacian, making them impractical at scale. We propose a simple and effective column-selective graph sampling algorithm based on a minimum inner product greedy selection rule. At each iteration, the algorithm accesses only a small random subset of Laplacian columns, requiring no eigendecomposition or global graph traversal, making it well-suited for large-scale graphs where the full Laplacian cannot be stored in memory. We analyze the algorithm under the stochastic block model and show that, when the degree distribution is balanced across nodes, the algorithm achieves sampling proportional to cluster size, and that the resulting mean estimate is controlled for band-limited graph signals in the Paley-Wiener space, with the error decaying as inter-cluster connectivity weakens. Numerical experiments on both synthetic and real-world data validate the effectiveness of the proposed method.

Problem

• graph coreset selection
• scalable sampling
• graph signal processing
• large-scale graphs
• representative node sampling

Innovation

• graph coreset selection
• greedy sampling
• graph signal processing
• scalable graph algorithms
• Laplacian column sampling