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High-Performance Spectral Methods For Computer-Aided Design Of Integrated Circuits, Zhiqiang Zhao

Dissertations, Master's Theses and Master's Reports

Recent research shows that by leveraging the key spectral properties of eigenvalues and eigenvectors of graph Laplacians, more efficient algorithms can be developed for tackling many graph-related computing tasks. In this dissertation, spectral methods are utilized for achieving faster algorithms in the applications of very-large-scale integration (VLSI) computer-aided design (CAD)

First, a scalable algorithmic framework is proposed 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 …