Dissertation/ Thesis
Cache locality exploiting methods and models for sparse matrix-vector multiplication
| Τίτλος: | Cache locality exploiting methods and models for sparse matrix-vector multiplication |
|---|---|
| Συγγραφείς: | Akbudak, Kadir |
| Έτος έκδοσης: | 2009 |
| Συλλογή: | Bilkent University: Institutional Repository |
| Θεματικοί όροι: | Cache locality, Sparse matrices, Matrix-vector multiplication, Matrix reordering, Computational hypergraph model, Hypergraph partitioning, Traveling salesman problem, QA188 .A53 2009, Sparse matrices--Data processing, Cache memory, Hypergraphs |
| Περιγραφή: | Cataloged from PDF version of article. ; Includes bibliographical references leaves 52-56. ; The sparse matrix-vector multiplication (SpMxV) is an important kernel operation widely used in linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers to solve a system of linear equations. High performance gains can be obtained if we can take the advantage of today’s deep cache hierarchy in SpMxV operations. Matrices with irregular sparsity patterns make it difficult to utilize data locality effectively in SpMxV computations. Different techniques are proposed in the literature to utilize cache hierarchy effectively via exploiting data locality during SpMxV. In this work, we investigate two distinct frameworks for cacheaware/oblivious SpMxV: single matrix-vector multiply and multiple submatrix-vector multiplies. For the single matrix-vector multiply framework, we propose a cache-size aware top-down row/column-reordering approach based on 1D sparse matrix partitioning by utilizing the recently proposed appropriate hypergraph models of sparse matrices, and a cache oblivious bottom-up approach based on hierarchical clustering of rows/columns with similar sparsity patterns. We also propose a column compression scheme as a preprocessing step which makes these two approaches cache-line-size aware. The multiple submatrix-vector multiplies framework depends on the partitioning the matrix into multiple nonzero-disjoint submatrices. For an effective matrixto-submatrix partitioning required in this framework, we propose a cache-size aware top-down approach based on 2D sparse matrix partitioning by utilizing the recently proposed fine-grain hypergraph model. For this framework, we also propose a traveling salesman formulation for an effective ordering of individual submatrix-vector multiply operations. We evaluate the validity of our models and methods on a wide range of sparse matrices. Experimental results show that proposed methods and models outperforms state-of-the-art schemes. ... |
| Τύπος εγγράφου: | thesis |
| Περιγραφή αρχείου: | xiv, 56 leaves; application/pdf |
| Γλώσσα: | English |
| Relation: | https://hdl.handle.net/11693/15336; B118111 |
| Διαθεσιμότητα: | https://hdl.handle.net/11693/15336 |
| Rights: | info:eu-repo/semantics/openAccess |
| Αριθμός Καταχώρησης: | edsbas.39D0640C |
| Βάση Δεδομένων: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://hdl.handle.net/11693/15336# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Header | DbId: edsbas DbLabel: BASE An: edsbas.39D0640C RelevancyScore: 762 AccessLevel: 3 PubType: Dissertation/ Thesis PubTypeId: dissertation PreciseRelevancyScore: 761.994323730469 |
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| Items | – Name: Title Label: Title Group: Ti Data: Cache locality exploiting methods and models for sparse matrix-vector multiplication – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Akbudak%2C+Kadir%22">Akbudak, Kadir</searchLink> – Name: DatePubCY Label: Publication Year Group: Date Data: 2009 – Name: Subset Label: Collection Group: HoldingsInfo Data: Bilkent University: Institutional Repository – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Cache+locality%22">Cache locality</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+matrices%22">Sparse matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix-vector+multiplication%22">Matrix-vector multiplication</searchLink><br /><searchLink fieldCode="DE" term="%22Matrix+reordering%22">Matrix reordering</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+hypergraph+model%22">Computational hypergraph model</searchLink><br /><searchLink fieldCode="DE" term="%22Hypergraph+partitioning%22">Hypergraph partitioning</searchLink><br /><searchLink fieldCode="DE" term="%22Traveling+salesman+problem%22">Traveling salesman problem</searchLink><br /><searchLink fieldCode="DE" term="%22QA188+%2EA53+2009%22">QA188 .A53 2009</searchLink><br /><searchLink fieldCode="DE" term="%22Sparse+matrices--Data+processing%22">Sparse matrices--Data processing</searchLink><br /><searchLink fieldCode="DE" term="%22Cache+memory%22">Cache memory</searchLink><br /><searchLink fieldCode="DE" term="%22Hypergraphs%22">Hypergraphs</searchLink> – Name: Abstract Label: Description Group: Ab Data: Cataloged from PDF version of article. ; Includes bibliographical references leaves 52-56. ; The sparse matrix-vector multiplication (SpMxV) is an important kernel operation widely used in linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers to solve a system of linear equations. High performance gains can be obtained if we can take the advantage of today’s deep cache hierarchy in SpMxV operations. Matrices with irregular sparsity patterns make it difficult to utilize data locality effectively in SpMxV computations. Different techniques are proposed in the literature to utilize cache hierarchy effectively via exploiting data locality during SpMxV. In this work, we investigate two distinct frameworks for cacheaware/oblivious SpMxV: single matrix-vector multiply and multiple submatrix-vector multiplies. For the single matrix-vector multiply framework, we propose a cache-size aware top-down row/column-reordering approach based on 1D sparse matrix partitioning by utilizing the recently proposed appropriate hypergraph models of sparse matrices, and a cache oblivious bottom-up approach based on hierarchical clustering of rows/columns with similar sparsity patterns. We also propose a column compression scheme as a preprocessing step which makes these two approaches cache-line-size aware. The multiple submatrix-vector multiplies framework depends on the partitioning the matrix into multiple nonzero-disjoint submatrices. For an effective matrixto-submatrix partitioning required in this framework, we propose a cache-size aware top-down approach based on 2D sparse matrix partitioning by utilizing the recently proposed fine-grain hypergraph model. For this framework, we also propose a traveling salesman formulation for an effective ordering of individual submatrix-vector multiply operations. We evaluate the validity of our models and methods on a wide range of sparse matrices. Experimental results show that proposed methods and models outperforms state-of-the-art schemes. ... – Name: TypeDocument Label: Document Type Group: TypDoc Data: thesis – Name: Format Label: File Description Group: SrcInfo Data: xiv, 56 leaves; application/pdf – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: https://hdl.handle.net/11693/15336; B118111 – Name: URL Label: Availability Group: URL Data: https://hdl.handle.net/11693/15336 – Name: Copyright Label: Rights Group: Cpyrght Data: info:eu-repo/semantics/openAccess – Name: AN Label: Accession Number Group: ID Data: edsbas.39D0640C |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.39D0640C |
| RecordInfo | BibRecord: BibEntity: Languages: – Text: English Subjects: – SubjectFull: Cache locality Type: general – SubjectFull: Sparse matrices Type: general – SubjectFull: Matrix-vector multiplication Type: general – SubjectFull: Matrix reordering Type: general – SubjectFull: Computational hypergraph model Type: general – SubjectFull: Hypergraph partitioning Type: general – SubjectFull: Traveling salesman problem Type: general – SubjectFull: QA188 .A53 2009 Type: general – SubjectFull: Sparse matrices--Data processing Type: general – SubjectFull: Cache memory Type: general – SubjectFull: Hypergraphs Type: general Titles: – TitleFull: Cache locality exploiting methods and models for sparse matrix-vector multiplication Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Akbudak, Kadir IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2009 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa |
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