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New spectral methods for ratio cut partition and clustering (1992)
| Venue: | IEEE TRANS. ON COMPUTER-AIDED DESIGN |
| Citations: | 292 - 17 self |
BibTeX
@ARTICLE{Hagen92newspectral,
author = {Lars Hagen and Andrew B. Kahng},
title = {New spectral methods for ratio cut partition and clustering},
journal = {IEEE TRANS. ON COMPUTER-AIDED DESIGN},
year = {1992},
pages = {1074--1085}
}
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Abstract
Partitioning of circuit netlists is important in many phases of VLSI design, ranging from layout to testing and hardware simulation. The ratio cut objective function [29] has received much attention since it naturally captures both min-cut and equipartition, the two traditional goals of partitioning. In this paper, we show that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approx-imation of the optimal ratio cut partition cost. We also dem-onstrate that fast Lanczos-type methods for the sparse sym-metric eigenvalue problem are a robust basis for computing heuristic ratio cuts based on the eigenvector of this second ei-genvalue. Effective clustering methods are an immediate by-product of the second eigenvector computation, and are very successful on the “difficult” input classes proposed in the CAD literature. Finally, we discuss the very natural intersection graph
Keyphrases
new spectral method ratio cut partition much attention many phase sparse sym-metric eigenvalue problem vlsi design robust basis second eigenvector computation effective clustering method heuristic ratio cut difficult input class immediate by-product cad literature ratio cut objective function circuit netlists good approx-imation fast lanczos-type method traditional goal optimal ratio cut partition cost hardware simulation natural intersection graph
