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Volumn 10, Issue 1, 1997, Pages 96-108

A variant of the Buchberger algorithm for integer programming

Author keywords

Buchberger algorithm; Gr bner bases; Integer programming; Iterative improvement heuristics; Test sets; Upper bounds

Indexed keywords


EID: 0012692786     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480195281209     Document Type: Article
Times cited : (18)

References (16)
  • 1
    • 0003723775 scopus 로고
    • B.I.-Wissenschaftsverlag, Bibliographisches Institut, Zürich, Cambridge University Press, London
    • TH. BETH, D. JUNGNICKEL, AND H. LENZ, Design Theory, B.I.-Wissenschaftsverlag, Bibliographisches Institut, Zürich, 1985; Cambridge University Press, London, 1993.
    • (1985) Design Theory
    • Beth, T.H.1    Jungnickel, D.2    Lenz, H.3
  • 2
    • 0004912313 scopus 로고
    • MIPLIB: A test set of mixed integer programming problems
    • available from Rice University SOFTLIB at softlib.cs.rice.edu and from ZIB eLib electronic library at elib.zib-berlin.de.
    • R. E. BIXBY, E. A. BOYD, AND R. R. INDOVINA, MIPLIB: A test set of mixed integer programming problems, SIAM News, 25 (1992), p. 16; available from Rice University SOFTLIB at softlib.cs.rice.edu and from ZIB eLib electronic library at elib.zib-berlin.de.
    • (1992) SIAM News , vol.25 , pp. 16
    • Bixby, R.E.1    Boyd, E.A.2    Indovina, R.R.3
  • 4
    • 0002803133 scopus 로고
    • Gröbner bases: An algorithmic method in polynomial ideal theory
    • N. K. Böse, ed., D. Reidel
    • B. BUCHBERGER, Gröbner bases: An algorithmic method in polynomial ideal theory, in Multi-dimensional Systems Theory, N. K. Böse, ed., D. Reidel, 1985, pp. 184-232.
    • (1985) Multi-dimensional Systems Theory , pp. 184-232
    • Buchberger, B.1
  • 5
    • 85030652056 scopus 로고
    • Buchberger algorithm and integer programming
    • P. CONTI AND C. TRAVERSO, Buchberger algorithm and integer programming, Lecture Notes in Comput. Sci., 539 (1991), pp. 130-139.
    • (1991) Lecture Notes in Comput. Sci. , vol.539 , pp. 130-139
    • Conti, P.1    Traverso, C.2
  • 6
    • 0003908675 scopus 로고
    • Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra
    • Springer-Verlag, New York
    • D. A. COX, J. B. LITTLE, AND D. O'SHEA, Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1992.
    • (1992) Undergraduate Texts in Mathematics
    • Cox, D.A.1    Little, J.B.2    O'Shea, D.3
  • 7
    • 0030303866 scopus 로고    scopus 로고
    • Solving multiple knapsack problems by cutting planes
    • C. E. FERREIRA, A. MARTIN, AND R. WEISMANTEL, Solving multiple knapsack problems by cutting planes, SIAM J. Optim., 6 (1996), pp. 858-877.
    • (1996) SIAM J. Optim. , vol.6 , pp. 858-877
    • Ferreira, C.E.1    Martin, A.2    Weismantel, R.3
  • 8
    • 85033319628 scopus 로고
    • Personal communication, Universität Dortmund
    • H. HEITKOTTER, Personal communication, Universität Dortmund, 1993.
    • (1993)
    • Heitkotter, H.1
  • 9
    • 0027614308 scopus 로고
    • Solving airline crew-scheduling problems by branch-and-cut
    • K. L. HUFFMAN AND M. PADBERG, Solving airline crew-scheduling problems by branch-and-cut, Management Science, 39 (1993), pp. 657-682.
    • (1993) Management Science , vol.39 , pp. 657-682
    • Huffman, K.L.1    Padberg, M.2
  • 10
    • 84948969856 scopus 로고
    • GRIN: An implementation of Gröbner bases for integer programming
    • S. HOŞTEN AND B. STURMFELS, GRIN: An implementation of Gröbner bases for integer programming, Lecture Notes in Comput. Sci., 920 (1995), pp. 267-276.
    • (1995) Lecture Notes in Comput. Sci. , vol.920 , pp. 267-276
    • Hoşten, S.1    Sturmfels, B.2
  • 11
    • 84990479742 scopus 로고
    • An efficient heuristic procedure for partitioning graphs
    • B. W. KERNIGHAN AND S. LIN, An efficient heuristic procedure for partitioning graphs, Bell Systems Technical Journal, 49 (1970), pp. 291-307.
    • (1970) Bell Systems Technical Journal , vol.49 , pp. 291-307
    • Kernighan, B.W.1    Lin, S.2
  • 12
    • 0015604699 scopus 로고
    • An effective heuristic algorithm for the traveling salesman problem
    • B. W. KERNIGHAN AND S. LIN, An effective heuristic algorithm for the traveling salesman problem, Oper. Res., 21 (1973), pp. 498-516.
    • (1973) Oper. Res. , vol.21 , pp. 498-516
    • Kernighan, B.W.1    Lin, S.2
  • 14
    • 0024681830 scopus 로고
    • On the facial structure of the set covering polytope
    • A. SASSANO, On the facial structure of the set covering polytope, Math. Programming, 44 (1989), pp. 181-202.
    • (1989) Math. Programming , vol.44 , pp. 181-202
    • Sassano, A.1
  • 15
    • 0001698976 scopus 로고
    • A geometric Buchberger algorithm for integer programming
    • R. R. THOMAS, A geometric Buchberger algorithm for integer programming, Math. Oper. Res., 20 (1995), pp. 864-884.
    • (1995) Math. Oper. Res. , vol.20 , pp. 864-884
    • Thomas, R.R.1
  • 16
    • 85033310066 scopus 로고    scopus 로고
    • Truncated Gröbner bases for integer programming
    • to appear
    • R. R. THOMAS AND R. WEISMANTEL, Truncated Gröbner bases for integer programming, AAECC, to appear.
    • AAECC
    • Thomas, R.R.1    Weismantel, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.