Reordering sparse matrices into block-diagonal column-overlapped form

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buir.contributor.authorAykanat, Cevdet
dc.citation.epage109en_US
dc.citation.spage99en_US
dc.citation.volumeNumber140en_US
dc.contributor.authorAcer, S.en_US
dc.contributor.authorAykanat, Cevdeten_US
dc.date.accessioned2021-02-25T07:03:46Z
dc.date.available2021-02-25T07:03:46Z
dc.date.issued2020
dc.departmentDepartment of Computer Engineeringen_US
dc.description.abstractMany scientific and engineering applications necessitate computing the minimum norm solution of a sparse underdetermined linear system of equations. The minimum 2-norm solution of such systems can be obtained by a recent parallel algorithm, whose numerical effectiveness and parallel scalability are validated in both shared- and distributed-memory architectures. This parallel algorithm assumes the coefficient matrix in a block-diagonal column-overlapped (BDCO) form, which is a variant of the block-diagonal form where the successive diagonal blocks may overlap along their columns. The total overlap size of the BDCO form is an important metric in the performance of the subject parallel algorithm since it determines the size of the reduced system, solution of which is a bottleneck operation in the parallel algorithm. In this work, we propose a hypergraph partitioning model for reordering sparse matrices into BDCO form with the objective of minimizing the total overlap size and the constraint of maintaining balance on the number of nonzeros of the diagonal blocks. Our model makes use of existing partitioning tools that support fixed vertices in the recursive bipartitioning paradigm. Experimental results validate the use of our model as it achieves small overlap size and balanced diagonal blocks.en_US
dc.description.provenanceSubmitted by Onur Emek (onur.emek@bilkent.edu.tr) on 2021-02-25T07:03:46Z No. of bitstreams: 1 Reordering_sparse_matrices_into_block-diagonal_column-overlapped_form.pdf: 2682291 bytes, checksum: 2e13c767bb5ea658cf468ea608e133a2 (MD5)en
dc.description.provenanceMade available in DSpace on 2021-02-25T07:03:46Z (GMT). No. of bitstreams: 1 Reordering_sparse_matrices_into_block-diagonal_column-overlapped_form.pdf: 2682291 bytes, checksum: 2e13c767bb5ea658cf468ea608e133a2 (MD5) Previous issue date: 2020en
dc.embargo.release2022-06-01
dc.identifier.doi10.1016/j.jpdc.2020.03.002en_US
dc.identifier.issn0743-7315
dc.identifier.urihttp://hdl.handle.net/11693/75577
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.jpdc.2020.03.002en_US
dc.source.titleJournal of Parallel and Distributed Computingen_US
dc.subjectUnderdetermined systemsen_US
dc.subjectSparse matricesen_US
dc.subjectBlock-diagonal formen_US
dc.subjectColumn overlapen_US
dc.subjectHypergraph partitioningen_US
dc.titleReordering sparse matrices into block-diagonal column-overlapped formen_US
dc.typeArticleen_US

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