한국경영과학회지 (Journal of the Korean Operations Research and Management Science Society)

  • 제21권3호
  • /
  • Pages.63-74
  • /
  • 1996
  • /
  • 1225-1119(pISSN)
  • /
  • 2733-4759(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
권호 표지

내부점기법에 있어서 효율적인 순서화와 자료구조(최소부족순서화를 중심으로)

An Efficient Ordering Method and Data Structure of the Interior Point Method (Putting Emphasis on the Minimum Deficiency Ordering

  • 박순달 (서울대학교 공과대학 산업공학과) ;
  • 김병규 (서울대학교 공과대학 산업공학과) ;
  • 성명기 (서울대학교 공과대학 산업공학과)
  • 발행 : 1996.12.01
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⟨ 이전 논문 다음 논문 ⟩

초록

Ordering plays an important role in solving an LP problem with sparse matrix by the interior point method. Since ordering is NP-complete, we try to find an efficient method. The objective of this paper is to present an efficient heuristic ordering method for implementation of the minimum deficiency method. Both the ordering method and the data structure play important roles in implementation. First we define a new heuristic pseudo-deficiency ordering method and a data structure for the method-quotient graph and cliqued storage. Next we show an experimental result in terms of time and nonzero numbers by NETLIB problems.

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참고문헌

  1. 서울대학교 대학원 산업공학과 석사학위 논문 내부점 선형계획법에서의 순서화 방법과 자료구조에 관한 연구 모정훈
  2. 선형계획법(3판) 박순달
  3. Direct Methods for Sparse Matrices Duff,I.S.;A.M.Erisman;J.K.Reid
  4. Computer Solution of Large Sparse Positive Definite Systems George,J.A.;J.W.H. Liu
  5. SIAM Review v.31 no.1 The Evolution of the Minimum Degree Ordering Algorithm George,J.A.;J.W.H.LIU
  6. Ph. D. Dissertation Direct Sparse Matrix Methods for Interior Point Algorithms Jung,H.W.
  7. Combinatorica v.4 no.4 A New Polynomial-Time Algorithm for Linear Programming karmarkar,N.
  8. ACM Transactions on Mathematical Software v.11 no.2 Modification of the Minimum-Degree Algorithm by Multiple Elimination Liu,J.W.H.
  9. Interfaces v.20 no.4 Interior Point Methods for Linear Programming: Just Call Newton Lagrange, and Fiacco & McCormick Marsten,R.;R.Subramanian;M.Saltzman