Skip to main content
SpringerLink
Log in

On the approximability of the Steiner tree problem in phylogeny

  • Session 3b: Invited Presentation
  • Conference paper
  • First Online:
Algorithms and Computation (ISAAC 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1178))

Included in the following conference series:

  • 157 Accesses

Abstract

Three results on the Steiner tree problem are presented: (i) Computing optimum k-restricted Steiner tree is APX-complete for k≥4, (ii) the minimum-cost k-restricted Steiner tree problem in phylogeny is APX-complete for k≥4, and (iii) the k-Steiner ratio for the Steiner tree problem in phylogeny matches the corresponding ratio for metric spaces defined on graphs. The results are significant because k-restricted trees are used in various approximation algorithms for the Steiner tree problem, and (i) and (ii) suggest that there is a limit to the approximability of the optimum solution. The k-Steiner ratio, which establishes a relation between the size of the optimum Steiner tree and the optimum k-restricted tree, arises in the analysis of many of the same algorithms.

Supported in part by the National Science Foundation under grants CCR-9211262 and CCR-9520946.

Supported by grants from NFR and TFR.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and hardness of approximation problems. In 33rd FOCS, pages 14–23, 1992.

    Google Scholar 

  2. P. Berman and V. Ramaiyer. Improved approximations for the Steiner tree problem. In 3rd SODA, pages 1–10, 1992.

    Google Scholar 

  3. H. Bodlaender, M. Fellows, and T. Warnow. Two strikes against perfect phylogeny. In Proceedings of the 19th International Colloquium on Automata, Languages, and Programming, pp. 273–283, Springer Verlag, Lecture Notes in Computer Science, 1992.

    Google Scholar 

  4. A. Borchers and D.-Z. Du. The k-Steiner ratio in graphs. In Proceedings 27th Annual Symposium on Theory of Computing, pp. 641–249.

    Google Scholar 

  5. W.H.E. Day, D.S. Johnson, and D. Sankoff. The computational complexity of inferring rooted phylogenies by parsimony. Mathematical Biosciences, 81:33–42, 1986.

    Article  Google Scholar 

  6. A. Dress and M. Steel. Convex tree realizations of partitions. Appl. Math. Letters, 5(3):3–6, 1992.

    Article  Google Scholar 

  7. D.-Z. Du and F.K. Hwang. An approach for proving lower bounds: solution of Gilbert-Pollack's conjecture on the Steiner ratio. Proceedings of the 31st Annual Symposium on Foundations of Computer Science, pp. 76–85, 1990.

    Google Scholar 

  8. G. F. Estabrook, C. S. Johnson Jr., and F. R. McMorris. An idealized concept of the true cladistic character. Mathematical Biosciences, 23:263–272, 1975.

    Article  Google Scholar 

  9. G. F. Estabrook. Cladistic methodology: A discussion of the theoretical basis for the induction of evolutionary history. Annual Review of Ecology and Systematics, 3:427–456, 1972.

    Article  Google Scholar 

  10. W. M. Fitch. Aspects of Molecular Evolution. Annual Reviews of Genetics, 7:343–380, 1973.

    Article  Google Scholar 

  11. L.R. Foulds and R.L. Graham. The Steiner tree problem in phylogeny is NP-complete. Advances in Applied Mathematics, 3:43–49, 1982.

    Article  Google Scholar 

  12. D. Gusfield. The Steiner tree problem in phylogeny. Unpublished manuscript.

    Google Scholar 

  13. J. Håstad, J. Lagergren, and V. Kann. Personal communication.

    Google Scholar 

  14. F.K. Hwang, D.S. Richards, and P. Winter. The Steiner Tree Problem. North-Holland, Amsterdam, 1992.

    Google Scholar 

  15. T. Jiang, E.L. Lawler, and L. Wang. Aligning sequences via an evolutionary tree: Complexity and approximation (extended abstract). In Proceedings of the Twenty-Sixth Annual ACM Symposium on Theory of Computing, pp. 760–769, Montréal, Québec, Canada, 1994.

    Google Scholar 

  16. S. Khanna, R. Motwani, M. Sudan, and U. Vazirani. On Syntactic versus Computational Views of Approximability. In 35th Annual Symposium on Foundations of Computer Science, pp. 819–830, Santa Fe, New Mexico, 1994.

    Google Scholar 

  17. C.H. Papadimitriou. Computational Complexity. Addison-Wesley, Reading, MA, 1994.

    Google Scholar 

  18. C.H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. Journal of Computer and System Sciences, 43. Also in STOC '88.

    Google Scholar 

  19. M.A. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. Journal of Classification, 9:91–116, 1992.

    Google Scholar 

  20. Tandy Warnow, Donald Ringe, and Ann Taylor. Reconstructing the evolutionary history of natural languages. To appear in Proc. SODA 96.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Iowa State University, 50011, Ames, IA

    David Fernández-Baca

  2. Department of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Jens Lagergren

Authors
  1. David Fernández-Baca
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jens Lagergren
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Tetsuo Asano Yoshihide Igarashi Hiroshi Nagamochi Satoru Miyano Subhash Suri

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fernández-Baca, D., Lagergren, J. (1996). On the approximability of the Steiner tree problem in phylogeny. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009482

Download citation

  • DOI: https://doi.org/10.1007/BFb0009482

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62048-8

  • Online ISBN: 978-3-540-49633-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation