Fast and effective algorithms for graph partitioning and sparse-matrix ordering

Gupta, Anshul

doi:10.1147/rd.411.0171

Cited by 87 publications

(67 citation statements)

References 27 publications

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“…WSMP uses the Pthread libray and PARDISO uses the OpenMP parallel directives. Both solver always permute the original matrix to maximize the product of diagonal elements and nested-dissection based fill-orderings has been used [11,14]. Two important observation can be drawn from the table.…”

Section: Resultsmentioning

confidence: 99%

“…The first is that WSMP needs in most of the examples less operations than PARDISO. It seems that the algorithm based on [11] produces orderings with a smaller fill-in compared with [14], which is used in PARDISO. The second observation is that the factorization times are affected by the preprocessing and WSMP is in most cases faster on a single Power 3 processor.…”

Section: Resultsmentioning

confidence: 99%

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Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO

Schenk

Gärtner

2002

Lecture Notes in Computer Science

142

154

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Abstract. Supernode pivoting for unsymmetric matrices coupled with supernode partitioning and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and prepermutation of rows is used to place large matrix entries on the diagonal. Supernode pivoting allows dynamical interchanges of columns and rows during the factorization process. The BLAS-3 level efficiency is retained. An enhanced left-right looking scheduling scheme is uneffected and results in good speedup on SMP machines without increasing the operation count. These algorithms have been integrated into the recent unsymmetric version of the PARDISO solver. Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsymmetric matrices from real world applications.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO

Schenk

Gärtner

2002

Lecture Notes in Computer Science

142

154

View full text Add to dashboard Cite

show abstract

“…Therefore, the algorithm can produce a good partition of the original graph. [14] argued that the HEM algorithm may miss some heavy edges in the graph because the nodes are visited randomly. To overcome this problem, they proposed a heaviestedge matching by sorting the edges by their weights and visiting them in decreasing order of weight.…”

Section: Graph Partitioning Algorithmmentioning

confidence: 99%

“…If r (instead of 2) nodes of the graph are coalesced into one at each coarsening step, the total number of steps can be reduced form log 2 (n/k) to log r (n/k). [14] used an algorithm called heavy-triangle matching (HTM), which coalesces three nodes at a time so that they can get 20% time saving.…”

Section: Graph Partitioning Algorithmmentioning

confidence: 99%

An Effective Data Placement Strategy for XML Documents

Zhu

2001

Lecture Notes in Computer Science

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Abstract. As XML is increasingly being used in Web applications, new technologies need to be investigated for processing XML documents with high performance. Parallelism is a promising solution for structured document processing and data placement is a major factor for system performance improvement in parallel processing. This paper describes an effective XML document data placement strategy. The new strategy is based on a multilevel graph partitioning algorithm with the consideration of the unique features of XML documents and query distributions. A new algorithm, which is based on XML query schemas to derive the weighted graph from the labelled directed graph presentation of XML documents, is also proposed. Performance analysis on the algorithm presented in the paper shows that the new data placement strategy exhibits low workload skew and a high degree of parallelism.Keywords: Data Placement, XML Documents, Graph Partitioning, and Parallel Data Processing. IntroductionAs a new markup language for structured documentation, XML (eXtensible Markup Language) is increasingly being used in Web applications because of its unique features in data representation and exchange. The main advantage of XML is that each XML file can have a semantic schema and makes it possible to define much more meaningful queries than simple, keyword-based retrievals. A recent survey shows that the number of XML business vocabularies has increased from 124 to over 250 in six months [1]. It can be expected that data in XML format would be largely available throughout the Web in the near future. As Web applications are time vulnerable, the increasing size of XML documents and the complexity of evaluating XML queries pose new performance challenges to existing information retrieval technologies. The use of parallelism has shown good scalability in traditional database applications and provides an attractive solution to process structured documents [2]. A large number of XML documents can be distributed onto several processing nodes so that a reasonable query response time can be achieved by processing the related data in parallel.

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“…Unfortunately, it also imposes serious limitations on the ability of multilevel algorithms to provide good quality partitionings. These limitations of the multilevel paradigm have been recently addressed in [7] and [11] using more dynamic coarsening strategies. In this paper, we present a broader strategy to address this issue.…”

mentioning

confidence: 99%

Multilevel cooperative search for the circuit/hypergraph partitioning problem

Ouyang

Toulouse

Thulasiraman

et al. 2002

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Abstract-The objectives in this paper are twofold: design an approach for the netlist partitioning problem using the cooperative multilevel search paradigm introduced by Toulouse et al. and study the effectiveness of this paradigm for solving combinatorial optimization problems, in particular, those arising in the very large scale integration (VLSI) computer-aided design (CAD) area. The authors present a cooperative multilevel search algorithm CoMHP and describe a parallel implementation on the SGI O2000 system. Experiments on ISPD98 benchmark suite of circuits show, for four-way and eight-way partitioning, a reduction of 3% to 15% in the size of hyperedge cuts compared to those obtained by hMETIS. Bisections of hypergraphs based on the algorithm also outperform hMETIS, although more modestly. The authors present experimental results to demonstrate that the cooperation scheme plays a key role in the performance of CoMHP. In fact, the improvement in the quality of the solutions produced by CoMHP is to a large extent independent of the partitioners used in the implementation of CoMHP. The experimental results also demonstrate the effectiveness of the cooperative multilevel search paradigm for solving the netlist partitioning problem and show that the cooperative multilevel search strategy can be used as a paradigm for designing effective solution techniques for combinatorial optimization problems such as those arising in the VLSI CAD area.

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Fast and effective algorithms for graph partitioning and sparse-matrix ordering

Cited by 87 publications

References 27 publications

Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO

Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO

An Effective Data Placement Strategy for XML Documents

Multilevel cooperative search for the circuit/hypergraph partitioning problem

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