Skip to main content
SpringerLink
Log in

The approximability of three-dimensional assignment problems with bottleneck objective

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

We discuss two special cases of the three-dimensional bottleneck assignment problem where a certain underlying cost function satisfies the triangle inequality. We present polynomial time 2-approximation algorithms for the broadest class of these special cases, and we prove that (unless P = NP) this factor 2 is best possible even in the highly restricted setting of the Euclidean plane.

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. Burkard, R., Dell’Amico, M., Martello, S.: Assignment problems. SIAM (2009)

  2. Crama Y., Spieksma F.C.R.: Approximation algorithms for three-dimensional assignment problems with triangle inequalities. Eur. J. Oper. Res. 60, 273–279 (1992)

    Article  MATH  Google Scholar 

  3. di Battista G., Eades P., Tamassia R., Tollis I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, Upper Saddle River (1999)

    MATH  Google Scholar 

  4. Dyer M.E., Frieze A.M.: Planar 3DM is NP-complete. J. Algorithms 7, 174–184 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  5. Feder, T., Greene, D.H.: Optimal algorithms for approximate clustering. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, pp. 434–444 (1988)

  6. González T.F.: Clustering to minimize the maximum intercluster distance. Theor. Comput. Sci. 38, 293–306 (1985)

    Article  MATH  Google Scholar 

  7. Hochbaum D.S., Shmoys D.B.: A unified approach to approximation algorithms for bottleneck problems. J. ACM 33, 533–550 (1986)

    Article  MathSciNet  Google Scholar 

  8. Klinz B., Woeginger G.J.: A new efficiently solvable special case of the three-dimensional axial bottleneck assignment problem. Lect. Notes Comput. Sci. 1120, 150–162 (1996)

    MathSciNet  Google Scholar 

  9. Malhotra R., Bhatia H.L., Puri M.C.: The three-dimensional bottleneck assignment problem and its variants. Optimization 16, 245–256 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  10. Queyranne M., Spieksma F.C.R.: Approximation algorithms for multi-index transportation problems with decomposable costs. Discret. Appl. Math. 76, 239–253 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Spieksma F.C.R., Woeginger G.J.: Geometric three-dimensional assignment problems. Eur. J. Oper. Res. 91, 611–618 (1996)

    Article  MATH  Google Scholar 

  12. Vartak M.N., Geetha S.: Specially structured precedence constraints in three-dimensional bottleneck assignment problems. J. Oper. Res. Soc. 41, 339–344 (1990)

    MATH  Google Scholar 

  13. Wang L., Du D.-Z.: Approximations for a bottleneck Steiner tree problem. Algorithmica 32, 554–561 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Operations Research Group, Katholieke Universiteit Leuven, Naamsestraat 69, 3000, Leuven, Belgium

    Dries Goossens, Sergey Polyakovskiy & Frits C. R. Spieksma

  2. Department of Mathematics, TU Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Dries Goossens
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sergey Polyakovskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Frits C. R. Spieksma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gerhard J. Woeginger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frits C. R. Spieksma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goossens, D., Polyakovskiy, S., Spieksma, F.C.R. et al. The approximability of three-dimensional assignment problems with bottleneck objective. Optim Lett 4, 7–16 (2010). https://doi.org/10.1007/s11590-009-0152-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-009-0152-7

Keywords

Search

Navigation