Similarity-Aware Spectral Sparsification by Edge Filtering

In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral sparsification methods first extract low-stretch spanning tree from the original graph to form the backbone of the sparsifier, and then recover small portions of spectrally-critical off-tree edges to the spanning tree to significantly improve the approximation quality. However, it is not clear how many off-tree edges should be recovered for achieving a desired spectral similarity level within the sparsifier. Motivated by recent graph signal processing techniques, this paper proposes a similarity-aware spectral graph sparsification framework that leverages efficient spectral off-tree edge embedding and filtering schemes to construct spectral sparsifiers with guaranteed spectral similarity (relative condition number) level. An iterative graph densification scheme is introduced to facilitate efficient and effective filtering of off-tree edges for highly ill-conditioned problems. The proposed method has been validated using various kinds of graphs obtained from public domain sparse matrix collections relevant to VLSI CAD, finite element analysis, as well as social and data networks frequently studied in many machine learning and data mining applications

Electrical and Computer Engineering Annual Report 2017

Early Career Awards Faculty Directory Faculty Highlights Special Report: Mobility at Michigan Tech Faculty Publications Staff Profile & Directory Graduate Student Research Accelerated Master\u27s Degree Graduate Student Awards & Degrees Undergraduate Highlights Senior Design Enterprise Undergraduate Student Awards & Advisory Grants & Contracts Departmental Statistics A Pioneer\u27s Storyhttps://digitalcommons.mtu.edu/ece-annualreports/1001/thumbnail.jp

A spectral graph sparsification approach to scalable vectorless power grid integrity verification

Vectorless integrity verification is becoming increasingly critical to robust design of nanoscale power delivery networks (PDNs). To dramatically improve efficiency and capability of vectorless integrity verifications, this paper introduces a scalable multilevel integrity verification framework by leveraging a hierarchy of almost linear-sized spectral power grid sparsifiers that can well retain effective resistances between nodes, as well as a recent graph-theoretic algebraic multigrid (AMG) algorithmic framework. As a result, vectorless integrity verification solution obtained on coarse level problems can effectively help find the solution of the original problem. Extensive experimental results show that the proposed vectorless verification framework can always efficiently and accurately obtain worst-case scenarios in even very large power grid designs