New spectral methods for ratio cut partitioning and clustering
Hagen, L.; Kahng, A.B.
Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on
Volume 11, Issue 9, Sep 1992 Page(s):1074 - 1085
Digital Object Identifier 10.1109/43.159993
Summary:Partitioning of circuit netlists in VLSI design is considered. It
is shown that the second smallest eigenvalue of a matrix derived from
the netlist gives a provably good approximation of the optimal ratio cut
partition cost. It is also demonstrated that fast Lanczos-type methods
for the sparse symmetric eigenvalue problem are a robust basis for
computing heuristic ratio cuts based on the eigenvector of this second
eigenvalue. 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. The intersection
graph representation of the circuit netlist is considered, as a basis
for partitioning, a heuristic based on spectral ratio cut partitioning
of the netlist intersection graph is proposed. The partitioning
heuristics were tested on industry benchmark suites, and the results
were good in terms of both solution quality and runtime. Several types
of algorithmic speedups and directions for future work are discussed
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