Effective-resistance preserving spectral reduction of graphs

Document Type

Conference Proceeding

Publication Date

2019

Department

Department of Electrical and Computer Engineering

Abstract

This paper proposes a scalable algorithmic framework for effective-resistance preserving spectral reduction of large undirected graphs. The proposed method allows computing much smaller graphs while preserving the key spectral (structural) properties of the original graph. Our framework is built upon the following three key components: a spectrum-preserving node aggregation and reduction scheme, a spectral graph sparsification framework with iterative edge weight scaling, as well as effective-resistance preserving post-scaling and iterative solution refinement schemes. By leveraging recent similarity-aware spectral sparsification method and graph-theoretic algebraic multigrid (AMG) Laplacian solver, a novel constrained stochastic gradient descent (SGD) optimization approach has been proposed for achieving truly scalable performance (nearly-linear complexity) for spectral graph reduction. We show that the resultant spectrally-reduced graphs can robustly preserve the first few nontrivial eigenvalues and eigenvectors of the original graph Laplacian and thus allow for developing highly-scalable spectral graph partitioning and circuit simulation algorithms.

Publisher's Statement

© 2019 Association for Computing Machinery. Publisher’s version of record: https://doi.org/10.1145/3316781.3317809

Publication Title

DAC '19 Proceedings of the 56th Annual Design Automation Conference 2019

ISBN

978-1-4503-6725-7

Link to Full Text

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