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      • Department of Computer Engineering
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      A recursive bipartitioning algorithm for permuting sparse square matrices into block diagonal form with overlap

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      Author
      Acer, S.
      Kayaaslan, E.
      Aykanat, Cevdet
      Date
      2013
      Source Title
      SIAM Journal on Scientific Computing
      Print ISSN
      1064-8275
      Publisher
      Society for Industrial and Applied Mathematics
      Volume
      35
      Issue
      1
      Pages
      C99 - C121
      Language
      English
      Type
      Article
      Item Usage Stats
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      113
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      Abstract
      We investigate the problem of symmetrically permuting a square sparse matrix into a block diagonal form with overlap. This permutation problem arises in the parallelization of an explicit formulation of the multiplicative Schwarz preconditioner and a more recent block overlapping banded linear solver as well as its application to general sparse linear systems. In order to formulate this permutation problem as a graph theoretical problem, we define a constrained version of the multiway graph partitioning by vertex separator (GPVS) problem, which is referred to as the ordered GPVS (oGPVS) problem. However, existing graph partitioning tools are unable to solve the oGPVS problem. So, we also show how the recursive bipartitioning framework can be utilized for solving the oGPVS problem. For this purpose, we propose a left-to-right bipartitioning approach together with a novel vertex fixation scheme so that existing 2-way GPVS tools that support fixed vertices can be effectively and efficiently utilized in the recursive bipartitioning framework. Experimental results on a wide range of matrices confirm the validity of the proposed approach. © 2013 Society for Industrial and Applied Mathematics.
      Keywords
      Block diagonal form with overlap
      Combinatorial scientific computing
      Graph partitioning by vertex separator
      Partitioning with fixed vertices
      Recursive bipartitioning
      Sparse square matrices
      Block diagonal
      Permalink
      http://hdl.handle.net/11693/21000
      Published Version (Please cite this version)
      http://dx.doi.org/10.1137/120861242
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      • Department of Computer Engineering 1410
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