# SF-GRASS: Solver-Free Graph Spectral Sparsification

arXiv: https://arxiv.org/abs/2008.07633 · HTML: https://mlsanity.com/paper/2008.07633/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2020.

## Built on by (most cited first, 4 of 4)

- [HyperEF: Spectral Hypergraph Coarsening by Effective-Resistance Clustering](https://mlsanity.com/paper/2210.14813/) (2022)
- [SF-SGL: Solver-Free Spectral Graph Learning from Linear Measurements](https://mlsanity.com/paper/2302.04384/) (2023)
- [inGRASS: Incremental Graph Spectral Sparsification via Low-Resistance-Diameter Decomposition](https://mlsanity.com/paper/2402.16990/) (2024)
- [SHyPar: A Spectral Coarsening Approach to Hypergraph Partitioning](https://mlsanity.com/paper/2410.10875/) (2024)

## Abstract (arXiv)

Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs, vectorless verification of power/thermal grids, representation learning of large graphs, etc. However, prior spectral graph sparsification methods rely on fast Laplacian matrix solvers that are usually challenging to implement in practice. This work, for the first time, introduces a solver-free approach (SF-GRASS) for spectral graph sparsification by leveraging emerging spectral graph coarsening and graph signal processing (GSP) techniques. We introduce a local spectral embedding scheme for efficiently identifying spectrally-critical edges that are key to preserving graph spectral properties, such as the first few Laplacian eigenvalues and eigenvectors. Since the key kernel functions in SF-GRASS can be efficiently implemented using sparse-matrix-vector-multiplications (SpMVs), the proposed spectral approach is simple to implement and inherently parallel friendly. Our extensive experimental results show that the proposed method can produce a hierarchy of high-quality spectral sparsifiers in nearly-linear time for a variety of real-world, large-scale graphs and circuit networks when compared with the prior state-of-the-art spectral method.