Skip to main content
Log in

Solving the maxcut problem by the global equilibrium search

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

The authors propose an approach to the solution of the maxcut problem. It is based on the global equilibrium search method, which is currently one of the most efficient discrete programming methods. The efficiency of the proposed algorithm is analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. F. Barahona, M. Grotschel, M. Junger, and G. Reinelt, “An application of combinatorial optimization to statistical physics and circuit layout design,” Oper. Res., 36, 493–513 (1988).

    Article  MATH  Google Scholar 

  2. K. C. Chang and D.H.-C. Du, “Efficient algorithms for layer assignment problem,” IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, 6, 67–78 (1987).

    Article  Google Scholar 

  3. S. Poljak and Z. Tuza, “Maximum cuts and large bipartite subgraphs,” DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 20, 181–244 (1995).

    MathSciNet  Google Scholar 

  4. V. P. Shilo, “The method of global equilibrium search,” Cybern. Syst. Analysis, 35, No. 1, 68–74 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  5. I. V. Sergienko and V. P. Shilo, Discrete Optimization Problems: Challenges, Solution Methods, and Studies [in Russian], Naukova Dumka, Kyiv (2003).

    Google Scholar 

  6. I. V. Sergienko and V. P. Shylo, “Problems of discrete optimization: Challenges and main approaches to solve them,” Cybern. Syst. Analysis, 42, No. 4, 465–482 (2006).

    Article  MATH  Google Scholar 

  7. P. Pardalos, O. Prokopyev, O. Shylo, and V. Shylo, “Global equilibrium search applied to the unconstrained binary quadratic optimization problem,” Optim. Methods and Software, 23, 129–140 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  8. O. Prokopyev, O. Shylo, and V. Shylo, “Solving weighted MAX-SAT via global equilibrium search,” Oper. Res. Lett., 36, No. 4, 434-438 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Burer, R. D. C. Monteiro, and Y. Zhang, “Rank-two relaxation heuristics for MAX-CUT and other binary quadratic programs,” SIAM J. Optim., 12, 503–521 (2002).

    Article  MathSciNet  Google Scholar 

  10. P. Festa, P. M. Pardalos, M. G. C. Resende, and C. C. Ribeiro, “Randomized heuristics for the maxcut problem,” Optim. Methods and Software, 17, 1033–1058 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  11. G. Palubeckis and V. Krivickiene, “Application of multistart tabu search to the Max-Cut problem,” in: Information Technology and Control, 2(31), Technologija, Kaunas (2004), pp. 29–35.

  12. M. X. Goemans and D. P. Williamson, “Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,” J. ACM, 42, 1115–1145 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Marti, A. Duarte, and M. Laguna, “Advanced scatter search for the Max-Cut problem, INFORMS J. Computing, 21, No. 1, 26–38 (2009).

    Article  MathSciNet  Google Scholar 

  14. C. Helmberg and F. Rendl, “A spectral bundle method for semidefinite programming,” SIAM J. Optim., 10, 673–696 (2000).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. V. Shylo.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 68–79,September–October 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shylo, V.P., Shylo, O.V. Solving the maxcut problem by the global equilibrium search. Cybern Syst Anal 46, 744–754 (2010). https://doi.org/10.1007/s10559-010-9256-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-010-9256-4

Keywords

Navigation