Locality aware reordering for sparse triangular solve

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buir.advisorAykanat, Cevdet
dc.contributor.authorTorun, Tuğba
dc.date.accessioned2016-01-08T20:18:30Z
dc.date.available2016-01-08T20:18:30Z
dc.date.issued2014
dc.descriptionAnkara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2014.en_US
dc.descriptionThesis (Master's) -- Bilkent University, 2014.en_US
dc.descriptionIncludes bibliographical references leaves 60-63.en_US
dc.description.abstractSparse Triangular Solve (SpTS) is a commonly used kernel in a wide variety of scientific and engineering applications. Efficient implementation of this kernel on current architectures that involve deep cache hierarchy is crucial for attaining high performance. In this work, we propose an effective framework for cache-aware SpTS. Solution of sparse linear symmetric systems utilizing the direct methods require the triangular solve of the form LUz = b, where L is lower triangular factor and U is upper triangular factor. For cache utilization, we reorder the rows and columns of the L factor regarding the data dependencies of the triangular solve. We represent the data dependencies of the triangular solve as a directed hypergraph and construct an ordered partitioning model on this structure. For this purpose, we developed a variant of Fiduccia-Mattheyses (FM) algorithm which respects the dependency constraints. We also adopt the idea of splitting L factors into dense and sparse components and solving them seperately with different autotuned kernels for achieving more flexibility in this process. We investigate the performance variation of different storage schemes of L factors and the corresponding sparse and dense components. We utilize autotuning provided by Optimized Sparse Kernel Interface (OSKI) to reduce performance degradation that incurs due to the gap between processors and memory speeds. Experiments performed on real-world datasets verify the effectiveness of the proposed framework.en_US
dc.description.provenanceMade available in DSpace on 2016-01-08T20:18:30Z (GMT). No. of bitstreams: 1 1.pdf: 78510 bytes, checksum: d85492f20c2362aa2bcf4aad49380397 (MD5)en
dc.description.statementofresponsibilityTorun, Tuğbaen_US
dc.embargo.release2016-09-08
dc.format.extentxi, 71 leaves, graphicsen_US
dc.identifier.itemidB148328
dc.identifier.urihttp://hdl.handle.net/11693/18351
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectSparse Matricesen_US
dc.subjectTriangular Solveen_US
dc.subjectCache Localityen_US
dc.subjectMatrix Reorderingen_US
dc.subjectHypergraph Partitioningen_US
dc.subjectDirected Hypergraphen_US
dc.subject.lccQA188 .T67 2014en_US
dc.subject.lcshSparse matrices.en_US
dc.subject.lcshTriangularization.en_US
dc.titleLocality aware reordering for sparse triangular solveen_US
dc.typeThesisen_US
thesis.degree.disciplineComputer Engineering
thesis.degree.grantorBilkent University
thesis.degree.levelMaster's
thesis.degree.nameMS (Master of Science)

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