Partitioning sparse matrices with eigenvectors of graphs
SIAM Journal on Matrix Analysis and Applications
Fundamentals of matrix computations
Fundamentals of matrix computations
Benchmarks for layout synthesis—evolution and current status
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
Modeling hypergraphs by graphs with the same mincut properties
Information Processing Letters
Partitioning very large circuits using analytical placement techniques
DAC '94 Proceedings of the 31st annual Design Automation Conference
Applied numerical linear algebra
Applied numerical linear algebra
Multilevel hypergraph partitioning: application in VLSI domain
DAC '97 Proceedings of the 34th annual Design Automation Conference
The ISPD98 circuit benchmark suite
ISPD '98 Proceedings of the 1998 international symposium on Physical design
Spectral partitioning with multiple eigenvectors
Discrete Applied Mathematics - Special volume on VLSI
Enhancing Data Locality by Using Terminal Propagation
HICSS '96 Proceedings of the 29th Hawaii International Conference on System Sciences Volume 1: Software Technology and Architecture
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Many fields, ranging from bioinformatics to databases to large-scale integrated circuits, deal with the interrelation between elementary objects. Objects are represented as vertices and the relationships between them are represented as nets (edges that connect two or more vertices) in the form of a hypergraph. We seek a placement of vertices that groups like objects and separates unlike objects. This involves separating related objects into a few, possibly disjoint, blocks. These hypergraph-partitioning problems are NP-hard so cannot be solved exactly, except for very small instances. We develop and use a numerical technique based on eigenvector decomposition of the connectivity matrix associated with the circuit netlist to partition hypergraphs emanating from circuit netlists. The eigenvector components of the circuit connectivity matrix are then used to determine vertex coordinates in one dimension that are then rounded in some fashion to determine block assignments. The inherent difficulty with eigenvector techniques is that the eigenvector components tend to cluster, making it difficult to determine correct block assignments. Our technique uses weights on nets, vertices, and fixed vertices to obtain a more “discrete” placement of vertices, making it easier to determine correct block assignments.