Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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A New Ordering Method Using Elimination Trees

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  • Park, Chan-Kyoo (Knowledge & Information Technology Division, National Computerization Agency) ;
  • Doh, Seung-yong (Department of Industrial Engineering, Seoul National University) ;
  • Park, Soon-dal (Department of Industrial Engineering, Seoul National University)
  • 박찬규 (한국전산원 지식정보기술단) ;
  • 도승용 (서울대학교 산업공학과) ;
  • 박순달 (서울대학교 산업공학과)
  • Published : 2003.03.31
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Abstract

Ordering is performed to reduce the amount of fill-ins of the Cholesky factor of a symmetric positive definite matrix. This paper proposes a new ordering algorithm that reduces the fill-ins of the Cholesky factor iteratively by elimination tree rotations and clique separators. Elimination tree rotations have been used mainly to reorder the rows of the permuted matrix for the efficiency of storage space management or parallel processing, etc. In the proposed algorithm, however, they are repeatedly performed to reduce the fill-ins of the Cholesky factor. In addition, we presents a simple method for finding a minimal node separator between arbitrary two nodes of a chordal graph. The proposed reordering procedure using clique separators enables us to obtain another order of rows of which the number of till-ins decreases strictly.

Keywords

Acknowledgement

Supported by : 한국과학재단

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