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45
The ISPD98 Circuit Benchmark Suite
 Proc. ACM/IEEE Int’l Symp. Physical Design (ISPD 99), ACM
, 1998
"... From 19851993, the MCNC regularly introduced and maintained circuit benchmarks for use by the Design Automation community. However, during the last five years, no new circuits have been introduced that can be used for developing fundamental physical design applications, such as partitioning and pla ..."
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Cited by 127 (1 self)
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From 19851993, the MCNC regularly introduced and maintained circuit benchmarks for use by the Design Automation community. However, during the last five years, no new circuits have been introduced that can be used for developing fundamental physical design applications, such as partitioning and placement. The largest circuit in the existing set of benchmark suites has over 100,000 modules, but the second largest has just over 25,000 modules, which is small by today’s standards. This paper introduces the ISPD98 benchmark suite which consists of 18 circuits with sizes ranging from 13,000 to 210,000 modules. Experimental results for three existing partitioners are presented so that future researchers in partitioning can more easily evaluate their heuristics. 1
HypergraphPartitioning Based Decomposition for Parallel SparseMatrix Vector Multiplication
 IEEE Trans. on Parallel and Distributed Computing
"... In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph mo ..."
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Cited by 62 (34 self)
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In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the wellknown hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In the decomposition of the test matrices, the hypergraph models using PaToH and hMeTiS result in up to 63% less communication volume (30%38% less on the average) than the graph model using MeTiS, while PaToH is only 1.32.3 times slower than MeTiS on the average. ...
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 57 (19 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.
Improved Algorithms for Hypergraph Bipartitioning
 IN PROCEEDINGS OF THE ASIA AND SOUTH PACIFIC DESIGN AUTOMATION CONFERENCE
, 2000
"... Multilevel FiducciaMattheyses (MLFM) hypergraph partitioning [3, 22, 24] is a fundamental optimization in VLSI CAD physical design. The leading implementation, hMetis [23], has since 1997 proved itself substantially superior in both runtime and solution quality to even very recent works (e.g., [13, ..."
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Cited by 54 (15 self)
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Multilevel FiducciaMattheyses (MLFM) hypergraph partitioning [3, 22, 24] is a fundamental optimization in VLSI CAD physical design. The leading implementation, hMetis [23], has since 1997 proved itself substantially superior in both runtime and solution quality to even very recent works (e.g., [13, 17, 25]). In this work, we present two sets of results: (i) new techniques for flat FMbased hypergraph partitioning (which is the core of multilevel implementations), and (ii) a new multilevel implementation that offers leadingedge performance. Our new techniques for flat partitioning confirm the conjecture from [10], suggesting that specialized partitioning heuristics may be able to actively exploit fixed nodes in partitioning instances arising in the driving topdown placement context. Our FM variant is competitive with traditional FM on instances without terminals [1] and considerably superior on instances with fixed nodes (i.e., arising during topdown placement [8]). Our multilevel ...
Encapsulating Multiple CommunicationCost Metrics in Partitioning Sparse Rectangular Matrices for Parallel MatrixVector Multiplies
"... This paper addresses the problem of onedimensional partitioning of structurally unsymmetricsquare and rectangular sparse matrices for parallel matrixvector and matrixtransposevector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational load ..."
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Cited by 36 (22 self)
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This paper addresses the problem of onedimensional partitioning of structurally unsymmetricsquare and rectangular sparse matrices for parallel matrixvector and matrixtransposevector multiplies. The objective is to minimize the communication cost while maintaining the balance on computational loads of processors. Most of the existing partitioning models consider only the total message volume hoping that minimizing this communicationcost metric is likely to reduce other metrics. However, the total message latency (startup time) may be more important than the total message volume. Furthermore, the maximum message volume and latency handled by a single processor are also important metrics. We propose a twophase approach that encapsulates all these four communicationcost metrics. The objective in the first phase is to minimize the total message volume while maintainingthe computationalload balance. The objective in the second phase is to encapsulate the remaining three communicationcost metrics. We propose communicationhypergraph and partitioning models for the second phase. We then present several methods for partitioning communication hypergraphs. Experiments on a wide range of test matrices show that the proposed approach yields very effective partitioning results. A parallel implementation on a PC cluster verifies that the theoretical improvements shown by partitioning results hold in practice.
A finegrain hypergraph model for 2D decomposition of sparse matrices
 in: Proceedings of the 15th International Parallel and Distributed Processing Symposium, 2001, p. 118. C. Aykanat
"... We propose a new hypergraph model for the decomposition of irregular computational domains. This work focuses on the decomposition of sparse matrices for parallel matrixvector multiplication. However, the proposed model can also be used to decompose computational domains of other parallel reduction ..."
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Cited by 30 (10 self)
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We propose a new hypergraph model for the decomposition of irregular computational domains. This work focuses on the decomposition of sparse matrices for parallel matrixvector multiplication. However, the proposed model can also be used to decompose computational domains of other parallel reduction problems. We propose a “finegrain” hypergraph model for twodimensional decomposition of sparse matrices. In the proposed finegrain hypergraph model, vertices represent nonzeros and hyperedges represent sparsity patterns of rows and columns of the matrix. By partitioning the finegrain hypergraph into equally weighted vertex parts (processors) so that hyperedges are split among as few processors as possible, the model correctly minimizes communication volume while maintaining computationalload balance. Experimental results on a wide range of realistic sparse matrices confirm the validity of the proposed model, by achieving up to 50 percent better decompositionsthan the existing models, in terms of totalcommunication volume. 1
Hypergraphbased Dynamic Load Balancing for Adaptive Scientific Computations
"... Adaptive scientific computations require that periodic repartitioning (load balancing) occur dynamically to maintain load balance. Hypergraph partitioning is a successful model for minimizing communication volume in scientific computations, and partitioning software for the static case is widely ava ..."
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Cited by 23 (5 self)
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Adaptive scientific computations require that periodic repartitioning (load balancing) occur dynamically to maintain load balance. Hypergraph partitioning is a successful model for minimizing communication volume in scientific computations, and partitioning software for the static case is widely available. In this paper, we present a new hypergraph model for the dynamic case, where we minimize the sum of communication in the application plus the migration cost to move data, thereby reducing total execution time. The new model can be solved using hypergraph partitioning with fixed vertices. We describe an implementation of a parallel multilevel repartitioning algorithm within the Zoltan loadbalancing toolkit, which to our knowledge is the first code for dynamic load balancing based on hypergraph partitioning. Finally, we present experimental results that demonstrate the effectiveness of our approach on a Linux cluster with up to 64 processors. Our new algorithm compares favorably to the widely used ParMETIS partitioning software in terms of quality, and would have reduced total execution time in most of our test cases. ∗ Sandia is a multiprogram laboratory operated by Sandia Corporation,
On twodimensional sparse matrix partitioning: Models, methods, and a recipe
 SIAM J. Sci. Comput
, 2010
"... Abstract. We consider twodimensional partitioning of general sparse matrices for parallel sparse matrixvector multiply operation. We present three hypergraphpartitioningbased methods, each having unique advantages. The first one treats the nonzeros of the matrix individually and hence produces f ..."
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Cited by 22 (16 self)
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Abstract. We consider twodimensional partitioning of general sparse matrices for parallel sparse matrixvector multiply operation. We present three hypergraphpartitioningbased methods, each having unique advantages. The first one treats the nonzeros of the matrix individually and hence produces finegrain partitions. The other two produce coarser partitions, where one of them imposes a limit on the number of messages sent and received by a single processor, and the other trades that limit for a lower communication volume. We also present a thorough experimental evaluation of the proposed twodimensional partitioning methods together with the hypergraphbased onedimensional partitioning methods, using an extensive set of public domain matrices. Furthermore, for the users of these partitioning methods, we present a partitioning recipe that chooses one of the partitioning methods according to some matrix characteristics.
Parallel estimation of distribution algorithms
, 2002
"... The thesis deals with the new evolutionary paradigm based on the concept of Estimation of Distribution Algorithms (EDAs) that use probabilistic model of promising solutions found so far to obtain new candidate solutions of optimized problem. There are six primary goals of this thesis: 1. Suggestion ..."
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Cited by 22 (3 self)
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The thesis deals with the new evolutionary paradigm based on the concept of Estimation of Distribution Algorithms (EDAs) that use probabilistic model of promising solutions found so far to obtain new candidate solutions of optimized problem. There are six primary goals of this thesis: 1. Suggestion of a new formal description of EDA algorithm. This high level concept can be used to compare the generality of various probabilistic models by comparing the properties of underlying mappings. Also, some convergence issues are discussed and theoretical ways for further improvements are proposed. 2. Development of new probabilistic model and methods capable of dealing with continuous parameters. The resulting Mixed Bayesian Optimization Algorithm (MBOA) uses a set of decision trees to express the probability model. Its main advantage against the mostly used IDEA and EGNA approach is its backward compatibility with discrete domains, so it is uniquely capable of learning linkage between mixed continuousdiscrete genes. MBOA handles the discretization of continuous parameters as an integral part of the learning process, which outperforms the histogrambased