Skip to main content
SpringerLink
Log in

A Survey on Multiple Objective Minimum Spanning Tree Problems

  • Chapter
Book cover Algorithmics of Large and Complex Networks

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5515))

Abstract

We review the literature on minimum spanning tree problems with two or more objective functions (MOST) each of which is of the sum or bottleneck type. Theoretical aspects of different types of this problem are summarized and available algorithms are categorized and explained. The paper includes a concise tabular presentation of all the reviewed papers.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aggarwal, V., Aneja, Y.P., Nair, K.P.K.: Minimal spanning tree subject to a side constraint. Computers and Operations Research 9(4), 287–296 (1982)

    Article  Google Scholar 

  2. Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice-Hall, Inc., Englewood Cliffs (1993)

    MATH  Google Scholar 

  3. Andersen, K.A., Joernsten, K., Lind, M.: On bicriterion minimal spanning trees: an approximation. Computers and Operations Research 23, 1171–1182 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Camerini, P.M., Galbiati, G., Maffioli, F.: The complexity of multi-constrained spanning tree problems. In: Lovasz, L. (ed.) Theory of Algorithms, pp. 53–101. North-Holland, Amsterdam (1984)

    Google Scholar 

  5. Chen, G., Guo, W., Tu, X., Chen, H.: An improved algorithm to solve the multi-criteria minimum spanning tree problem. J. Softw. 17(3), 364–370 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Corley, H.W.: Efficient spanning trees. Journal of Optimization Theory and Applications 45(3), 481–485 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dell’Amico, M., Maffioli, F.: On some multicriteria arborescence problems: Complexity and algorithms. Discrete Applied Mathematics 65, 191–206 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dell’Amico, M., Maffioli, F.: Combining linear and non-linear objectives in spanning tree problems. Journal of Combinatorial Optimiation 4(2), 253–269 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Duin, C.W., Volgenant, A.: Minimum deviation and balanced optimization: A unified approach. Operations Research Letters 10, 43–48 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  11. Ehrgott, M., Gandibleux, X.: Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. Kluwer Academic Publishers, Boston (2002)

    MATH  Google Scholar 

  12. Ehrgott, M., Klamroth, K.: Connectedness of efficient solutions in multiple criteria combinatorial optimization. European Journal of Operational Research 97, 159–166 (1997)

    Article  MATH  Google Scholar 

  13. Gabow, H.N.: Two algorithms for generating weighted spanning trees in order. SIAM Journal on Computing 6, 139–150 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  14. Goemans, M.X., Ravi, R.: A constrained minimum spanning tree problem. In: Proccedings of the Scandinavian Workshop on Algorithmic Theory (SWAT), pp. 66–75. Springer, Heidelberg (1996)

    Google Scholar 

  15. Gorski, J., Klamroth, K., Ruzika, S.: Connectedness of efficient solutions in multiple objective combinatorial optimization. Report in Wirtschaftsmathematik, Nr. 102/2006, University of Kaiserslautern, Department of Mathematics (2006) (submitted for publication)

    Google Scholar 

  16. Gupta, S.K., Punnen, A.P.: Minimum deviation problems. Operations Research Letters 7, 201–204 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hamacher, H.W., Ruhe, G.: On spanning tree problems with multiple objectives. Annals of Operations Research 52, 209–230 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  18. Hassin, R., Levin, A.: An efficient polynomial time approximation scheme for the constrained minimum spanning tree problem using matroid intersection. SIAM Journal on Computing 33(2), 261–268 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  19. Henn, S.: The weight-constrained minimum spanning tree problem. Master’s thesis, Technische Universität Kaiserslautern (2007)

    Google Scholar 

  20. Hong, S.P., Chung, S.J., Park, B.H.: A fully polynomial bicriteria approximation scheme for the constrained spanning tree problem. Operations Research Letters 32, 233–239 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  21. Hutson, V.A., ReVelle, C.S.: Maximal direct covering tree problem. Transportation Science 23, 288–299 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hutson, V.A., ReVelle, C.S.: Indirect covering tree problems on spanning tree networks. European Journal of Operational Research 65, 20–32 (1993)

    Article  MATH  Google Scholar 

  23. Melamed, I.I., Sigal, I.K.: An investigation of linear convolution of criteria in multicriteria discrete programming. Computational Mathematics and Mathematical Physics 35(8), 1009–1017 (1995)

    MathSciNet  MATH  Google Scholar 

  24. Melamed, I.I., Sigal, I.K.: A computational investigation of linear parametrization of criteria in multicriteria discrete programming. Computational Mathematics and Mathematical Physics 36(10), 1341–1343 (1996)

    MathSciNet  MATH  Google Scholar 

  25. Melamed, I.I., Sigal, I.K.: Numerical analysis of tricriteria tree and assignment problems. Computational Mathematics and Mathematical Physics 38(10), 1707–1714 (1998)

    MathSciNet  MATH  Google Scholar 

  26. Melamed, I.I., Sigal, I.K.: Combinatorial optimization problems with two and three criteria. Doklady Mathematics 59(3), 490–493 (1999)

    MATH  Google Scholar 

  27. Minoux, M.: Solving combinatorial problems with combined min-max-min-sum objective and applications. Mathematical Programming 45, 361–372 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  28. Perny, P., Spanjaard, O.: A preference-based approach to spanning trees and shortest paths problems. European Journal of Operational Research 162(3), 584–601 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Punnen, A.P.: On combined minmax-minsum optimization. Computers and Operations Research 21, 707–716 (1994)

    Article  MATH  Google Scholar 

  30. Punnen, A.P., Nair, K.P.K.: A \(\mathcal{O}(m \log n)\) algorithm for the max + sum spanning tree problem. European Journal of Operational Research 89, 423–426 (1996)

    Article  MATH  Google Scholar 

  31. Ramos, R.M., Alonso, S., Sicilia, J., Gonzalez, C.: The problem of the optimal biobjective spanning tree. European Journal of Operational Research 111, 617–628 (1998)

    Article  MATH  Google Scholar 

  32. Ruzika, S.: On Multiple Objective Combinatorial Optimization. Ph.D thesis, Technische Universität Kaiserslautern (2007)

    Google Scholar 

  33. Schweigert, D.: Linear extensions and efficient trees. Preprint 172, University of Kaiserslautern, Department of Mathematics (1990)

    Google Scholar 

  34. Schweigert, D.: Linear extensions and vector-valued spanning trees. Methods of Operations Research 60, 219–222 (1990)

    MathSciNet  MATH  Google Scholar 

  35. Sergienko, I.V., Perepelitsa, V.A.: Finding the set of alternatives in discrete multicriterion problems. Kibernetika 5, 85–93 (1987)

    MATH  Google Scholar 

  36. Shogan, A.: Constructing a minimal-cost spanning tree subject to resource constraints and flow requirements. Networks 13, 169–190 (1983)

    Article  MathSciNet  Google Scholar 

  37. Steiner, S., Radzik, T.: Solving the biobjective minimum spanning tree problem using k-best algorithm. Technical Report TR-03-06, Department of Computers Science, King’s College, London, UK (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kaiserslautern, P.O. Box 3049, D-67653, Kaiserslautern, Germany

    Stefan Ruzika & Horst W. Hamacher

Authors
  1. Stefan Ruzika
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Horst W. Hamacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer & Information Science, University of Konstanz, 78457, Konstanz, Germany

    Jürgen Lerner

  2. Institute of Theoretical Informatics, Technical University of Karlsruhe, 76128, Karlsruhe, Germany

    Dorothea Wagner

  3. Department of Biological Physics, Eötvös Lorand University, Pazmany P. Stny 1A, 1117, Budapest, Hungary

    Katharina A. Zweig

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ruzika, S., Hamacher, H.W. (2009). A Survey on Multiple Objective Minimum Spanning Tree Problems. In: Lerner, J., Wagner, D., Zweig, K.A. (eds) Algorithmics of Large and Complex Networks. Lecture Notes in Computer Science, vol 5515. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02094-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02094-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02093-3

  • Online ISBN: 978-3-642-02094-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation