Cybernetics and Systems Analysis

, Volume 42, Issue 1, pp 54–64 | Cite as

New quadratic models for the maximum weighted cut problem

  • P. I. Stetsyuk


New quadratic models are proposed to improve the upper-bound estimates in the maximum weighted cut problem. They are found by two original methods for deriving redundant quadratic constraints. A well-known linear model is shown to follow from the models proposed. Recommendations on how to develop its strengthened analogs are given.


maximum weighted cut problem quadratic model Lagrangian dual quadratic estimate functionally redundant quadratic constraints 


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  1. 1.
    M. G. Garey and D. S. Johnson, Computers and Intractability. A Guide to the Theory of NP-completeness, W. H. Freeman & Co., San Francisco (1979).Google Scholar
  2. 2.
    N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer, Dordrecht (1998).Google Scholar
  3. 3.
    N. Z. Shor and O. A. Berezovskii, “New algorithms for the weighted maximum cut problem on graphs,” Cybern. Syst. Analysis, 31, No. 2, 240–245 (1995).zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    C. Delorme and S. Poljak, “Laplacian eigenvalues and the maximum cut problem,” Math. Program., 62, 557–574 (1993).zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    P. I. Stetsyuk, “Functionally redundant constraints for Boolean quadratic-type optimization problems,” Cybern. Syst. Analysis, 41, No. 6, 932–935 (2005).CrossRefGoogle Scholar
  6. 6.
    F. Barahona and A. R. Mahjoub, “On the cut polytope,” Math. Program., 36, 157–173 (1986).zbMATHMathSciNetGoogle Scholar
  7. 7.
    M. Laurent and F. Rendl, “Semidefinite programming and integer programming,” in: Rep. CWI, PNA-R0210, Amsterdam (2002).Google Scholar
  8. 8.
    M. Grotschel, L. Lovasz, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, Berlin (1988).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • P. I. Stetsyuk
    • 1
  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKievUkraine

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