Skip to main content
SpringerLink
Log in

Minimax problems of discrete optimization invariant under majority operators

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

A special class of discrete optimization problems that are stated as a minimax modification of the constraint satisfaction problem is studied. The minimax formulation of the problem generalizes the classical problem to realistic situations where the constraints order the elements of the set by the degree of their feasibility, rather than defining a dichotomy between feasible and infeasible subsets. The invariance of this ordering under an operator is defined, and the discrete minimization of functions invariant under majority operators is proved to have polynomial complexity. A particular algorithm for this minimization is described.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Bulatov and P. Jeavons, “Tractable constraints closed under a binary operation,” Technical Report PGR-TR-12-00 (Oxford University Computing Laboratory, Oxford, 2000).

    Google Scholar 

  2. A. Bulatov, “Tractable conservative constraint satisfaction problems,” Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science LICS’03 (Washington, DC, USA, 2003).

    Google Scholar 

  3. A. Bulatov, “Complexity of conservative constraint satisfaction problems,” ACM Trans. Comput. Logic 12(4), 24:1–24:66, July (2011).

    Article  MathSciNet  Google Scholar 

  4. F. Rossi, P. van Beek, and T. Walsh, Handbook of Constraint Programming (Elsevier Science, New York, 2006).

    MATH  Google Scholar 

  5. M. I. Schlesinger and B. Flach, “Some solvable subclasses of structural recognition problems,” Czech Pattern Recognition Workshop (2000).

    Google Scholar 

  6. O. A. Shcherbina, “Constraint satisfaction and constraint programming,” Intellekt. Sist. 15(1–4), 53–170 (2011).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Scientific Educational Center, pr. Akademika Glushkova 40, Kiev, 03680, Ukraine

    E. V. Vodolazskii & M. I. Schlesinger

  2. Czech Technical University in Prague, Zikova 4, Prague, 16636, Czech Republic

    B. Flach

Authors
  1. E. V. Vodolazskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Flach
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. I. Schlesinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. V. Vodolazskii.

Additional information

Original Russian Text © E.V. Vodolazskii, B. Flach, M.I. Schlesinger, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 8, pp. 1368–1378.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vodolazskii, E.V., Flach, B. & Schlesinger, M.I. Minimax problems of discrete optimization invariant under majority operators. Comput. Math. and Math. Phys. 54, 1327–1336 (2014). https://doi.org/10.1134/S0965542514080144

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542514080144

Keywords

Search

Navigation