Results 1  10
of
11
New spectral methods for ratio cut partition and clustering
 IEEE TRANS. ON COMPUTERAIDED DESIGN
, 1992
"... 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 mincut and equipartition, the two traditional goals of partitionin ..."
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Cited by 297 (17 self)
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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 mincut 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 approximation of the optimal ratio cut partition cost. We also demonstrate that fast Lanczostype 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 byproduct 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
Permuting Sparse Rectangular Matrices into BlockDiagonal Form
 SIAM Journal on Scientific Computing
, 2002
"... We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. W ..."
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Cited by 56 (18 self)
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We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose bipartite graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Our experiments on a wide range of matrices, using stateoftheart graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime.
Net Partitions Yield Better Module Partitions
 IEEE 29th Design Automation Conference
, 1992
"... In this paper, we demonstrate that the "dual" intersection graph of the netlist strongly captures circuit properties relevant to partitioning. We apply this transformation within an existing testbed that uses an eigenvector computation to derive a linear ordering of nets, rather than modul ..."
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Cited by 26 (8 self)
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In this paper, we demonstrate that the "dual" intersection graph of the netlist strongly captures circuit properties relevant to partitioning. We apply this transformation within an existing testbed that uses an eigenvector computation to derive a linear ordering of nets, rather than modules [12]. We then find a good module partition with respect to the ratio cut metric [23] via a sequence of incremental independentset computations in bipartite graphs derived from the net ordering. An efficient matchingbased algorithm called IGMatch was tested on MCNC benchmark circuits as well as additional industry examples. Results are very encouraging: the algorithm yields an average of 28.8% improvement over the results of [23]. The intersection graph representation also yields speedups over, e.g., the method of [11], due to additional sparsity in the netlist representation. 1 1 Preliminaries A standard model for VLSI layout associates a graph G = (V; E) with the circuit netlist; vertices in...
HYPERGRAPH PARTITIONINGBASED FILLREDUCING ORDERING
, 2009
"... A typical first step of a direct solver for linear system Mx = b is reordering of symmetric matrix M to improve execution time and space requirements of the solution process. In this work, we propose a novel nesteddissectionbased ordering approach that utilizes hypergraph partitioning. Our approac ..."
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Cited by 12 (5 self)
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A typical first step of a direct solver for linear system Mx = b is reordering of symmetric matrix M to improve execution time and space requirements of the solution process. In this work, we propose a novel nesteddissectionbased ordering approach that utilizes hypergraph partitioning. Our approach is based on formulation of graph partitioning by vertex separator (GPVS) problem as a hypergraph partitioning problem. This new formulation is immune to deficiency of GPVS in a multilevel framework hence enables better orderings. In matrix terms, our method relies on the existence of a structural factorization of the input M matrix in the form of M = AAT (or M = AD2AT). We show that the partitioning of the rownet hypergraph representation of rectangular matrix A induces a GPVS of the standard graph representation of matrix M. In the absence of such factorization, we also propose simple, yet effective structural factorization techniques that are based on finding an edge clique cover of the standard graph representation of matrix M, and hence applicable to any arbitrary symmetric matrix M. Our experimental evaluation has shown that the proposed method achieves better ordering in comparison to stateoftheart graphbased ordering tools even for symmetric matrices where structural M = AAT factorization is not provided as an input. For matrices coming from linear programming problems, our method enables even faster and better orderings.
Hypergraph partitioning through vertex separators on graphs
, 2010
"... The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computing. The ..."
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Cited by 2 (2 self)
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The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computing. The modeling flexibility of hypergraphs however, comes at a cost: algorithms on hypergraphs are inherently more complicated than those on graphs, which sometimes translate to nontrivial increases in processing times. Neither the modeling flexibility of hypergraphs, nor the runtime efficiency of graph algorithms can be overlooked. Therefore, the new research thrust should be how to cleverly tradeoff between the two. This work addresses one method for this tradeoff by solving the hypergraph partitioning problem by finding vertex separators on graphs. Specifically, we investigate how to solve the hypergraph partitioning problem by seeking a vertex separator on its net intersection graph (NIG), where each net of the hypergraph is represented by a vertex, and two vertices share an edge if their nets have a common vertex. We propose a vertexweighting scheme to attain good nodebalanced hypergraphs, since NIG model cannot preserve node balancing information. Vertexremoval and vertexsplitting techniques are described to optimize cutnet and connectivity metrics, respectively, under the recursive bipartitioning paradigm. We also developed an
MultiObjective Search Based Algorithms for Circuit Partitioning Problems
 Proc. of the 10th IEEE Int. confernce on VLSI Design
, 1997
"... Speeding up logic simulation is important to reduce design time of complex systems. Hardware emulation through reconfigurable systems(RS) build using FPGA's offer an cheap and efficient method to achieve the required speedup. Emulation through RS poses some unique problems because of the limit ..."
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Cited by 1 (1 self)
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Speeding up logic simulation is important to reduce design time of complex systems. Hardware emulation through reconfigurable systems(RS) build using FPGA's offer an cheap and efficient method to achieve the required speedup. Emulation through RS poses some unique problems because of the limited circuit and I/O resources. A preparatory step for emulation using RS is to partition the circuit into as few parts as possible satisfying the resource constraints. This paper presents multiobjective search based optimal and approximate algorithms for circuit partitioning for this purpose. 1
PARTITIONING HYPERGRAPHS IN SCIENTIFIC COMPUTING APPLICATIONS THROUGH VERTEX SEPARATORS ON GRAPHS
"... Abstract. The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computi ..."
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Abstract. The modeling flexibility provided by hypergraphs has drawn a lot of interest from the combinatorial scientific community, leading to novel models and algorithms, their applications, and development of associated tools. Hypergraphs are now a standard tool in combinatorial scientific computing. The modeling flexibility of hypergraphs however, comes at a cost: algorithms on hypergraphs are inherently more complicated than those on graphs, which sometimes translates to nontrivial increases in processing times. Neither the modeling flexibility of hypergraphs, nor the runtime efficiency of graph algorithms can be overlooked. Therefore, the new research thrust should be how to cleverly tradeoff between the two. This work addresses one method for this tradeoff by solving the hypergraph partitioning problem by finding vertex separators on graphs. Specifically, we investigate how to solve the hypergraph partitioning problem by seeking a vertex separator on its net intersection graph (NIG), where each net of the hypergraph is represented by a vertex, and two vertices share an edge if their nets have a common vertex. We propose a vertexweighting scheme to attain good nodebalanced hypergraphs, since the NIG model cannot preserve node balancing information. Vertexremoval and vertexsplitting techniques are described to optimize cutnet and connectivity metrics, respectively, under the recursive bipartitioning paradigm. We also developed implementations of our proposed hypergraph partitioning formulations by adopting and modifying a stateoftheart graph partitioning by vertex separator tool onmetis. Experiments conducted on a large collection of sparse matrices demonstrate the effectiveness of our proposed techniques. Key words. hypergraph partitioning; combinatorial scientific computing; graph partitioning by vertex separator; sparse matrices. AMS subject classifications.