• About
  • Policies
  • What is openaccess
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • University Library
      • Bilkent Theses
      • Theses - Department of Computer Engineering
      • Dept. of Computer Engineering - Master's degree
      • View Item
      •   BUIR Home
      • University Library
      • Bilkent Theses
      • Theses - Department of Computer Engineering
      • Dept. of Computer Engineering - Master's degree
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      A recursive graph bipartitioning algorithm by vertex separators with fixed vertices for permuting sparse matrices into block diagonal form with overlap

      Thumbnail
      View / Download
      4.0 Mb
      Author
      Acer, Seher
      Advisor
      Aykanat, Cevdet
      Date
      2011
      Publisher
      Bilkent University
      Language
      English
      Type
      Thesis
      Item Usage Stats
      103
      views
      44
      downloads
      Abstract
      Solving sparse system of linear equations Ax=b using preconditioners can be effi- ciently parallelized using graph partitioning tools. In this thesis, we investigate the problem of permuting a sparse matrix into a block diagonal form with overlap which is to be used in the parallelization of the multiplicative schwarz preconditioner. A matrix is said to be in block diagonal form with overlap if the diagonal blocks may overlap. In order to formulate this permutation problem as a graph-theoretical problem, we introduce a restricted version of the graph partitioning by vertex separator problem (GPVS), where the objective is to find a vertex partition whose parts are only connected by a vertex separator. The modified problem, we refer as ordered GPVS problem (oGPVS), is restricted such that the parts should exhibit an ordered form where the consecutive parts can only be connected by a separator. The existing graph partitioning tools are unable to solve the oGPVS problem. Thus, we present a recursive graph bipartitioning algorithm by vertex separators together with a novel vertex fixation scheme so that a GPVS tool supporting fixed vertices can effectively and efficiently be utilized. We also theoretically verified the correctness of the proposed approach devising a necessary and sufficient condition to the feasibility of a oGPVS solution. Experimental results on a wide range of matrices confirm the validity of the proposed approach.
      Keywords
      Graph partitioning by vertex separator
      Combinatorial scientific computing
      Parallel computing
      Block diagonal form with overlap
      Permalink
      http://hdl.handle.net/11693/15772
      Collections
      • Dept. of Computer Engineering - Master's degree 511
      Show full item record

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartments

      My Account

      Login

      Statistics

      View Usage StatisticsView Google Analytics Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the site administrator. Phone: (312) 290 1771
      Copyright © Bilkent University - Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin | Privacy