Skip to main content
SpringerLink
Log in
Book cover

Annual Symposium on Theoretical Aspects of Computer Science

STACS 1997: STACS 97 pp 559–570Cite as

RNC-approximation algorithms for the steiner problem

  • Algorithms IV
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

Abstract

In this paper we present an RNC-algorithm for finding a minimum spanning tree in a weighted 3-uniform hypergraph, assuming the edge weights are given in unary, and a fully polynomial time randomized approximation scheme if the edge weights are given in binary. From this result we then derive RNC-approximation algorithms for the Steiner problem in networks with approximation ratio (1+ε) 5/3 for all ε>0.

Supported in part by DFG grant Pr 296/4

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

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, Proc. 33rd Annual IEEE Symp. Foundations of Computer Science (1992), 14–23.

    Google Scholar 

  2. P. Berman and V. Ramaiyer, Improved Approximations for the Steiner Tree Problem, Journal of Algorithms17 (1994), 381–408.

    Article  Google Scholar 

  3. M. Bern and P. Plassmann, The Steiner problem with edge lengths 1 and 2, Information Processing Letters32 (1989), 171–176.

    Article  Google Scholar 

  4. A. Borchers and D.-Z. Du, The k-Steiner ratio in graphs, Proc. 27th Annual ACM Symp. on the Theory of Computing (1995), 641–649.

    Google Scholar 

  5. P.M. Camerini, G. Galbiati, and F. Maffioli, Random pseudo-polynomial algorithms for exact matroid problems, Journal of Algorithms13 (1992), 258–273.

    Article  Google Scholar 

  6. Choukhmane El-Arbi, Une heuristique pour le problème de l'arbre de Steiner, R.A.I.R.O. Recherche opérationnelle12 (1978), 207–212.

    Google Scholar 

  7. D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, Proc. 19th Annual ACM Symp. on Theory of Computing (1987), 1–6.

    Google Scholar 

  8. S.E. Dreyfus and R.A. Wagner, The Steiner problem in graphs, Networks1 (1972), 195–207.

    Google Scholar 

  9. D.-Z. Du, Y.-J. Zhang and Q. Feng, On better heuristic for Euclidean Steiner minimum trees, Proc. 32nd Annual IEEE Symp. on Foundations of Computer Science (1991), 431–439.

    Google Scholar 

  10. H.N. Gabow, Z. Galil, T.H. Spencer, Efficient implementation of graph algorithms using contraction, Proc. 25th Annual IEEE Symp. on Foundations of Computer Science (1984), 347–357.

    Google Scholar 

  11. H.N. Gabow and M. Stallmann, An augmenting path algorithm for linear matroid parity, Combinatorica6 (1986), 123–150.

    Google Scholar 

  12. R. Karp, Reducibility among combinatorial problems, in: Complexity of computer computations (Miller, R.E., Thatcher, J.W., eds.), Plenum Press, 1972, 85–103.

    Google Scholar 

  13. M. Karpinski and A.Z. Zelikovsky, New approximation algorithms for the Steiner tree problem, Electr. Colloq. Comput. Compl., TR95-030, 1995.

    Google Scholar 

  14. L. Kou, G. Markowsky, and L. Berman, A fast algorithm for Steiner trees, Acta Informatica15 (1981), 141–145.

    Article  Google Scholar 

  15. S. Lang, Algebra, Addison-Wesley Publishing Company, 1993.

    Google Scholar 

  16. L. Lovász, The matroid matching problem, Algebraic Methods in Graph Theory, Colloquia Mathematica Societatis János Bolyai, Szeged (Hungary), 1978.

    Google Scholar 

  17. L. Lovász, On determinants, matchings and random algorithms, Fund. Comput. Theory79 (1979), 565–574.

    Google Scholar 

  18. K. Mulmuley, U. Vazirani, and V. Vazirani, Matching is as easy as matrix inversion, Combinatorica7 (1987), 105–113.

    Google Scholar 

  19. V. Pan, Fast and efficient algorithms for the exact inversion of integer matrices, Fifth Annual Foundations of Software Technology and Theoretical Computer Science Conference (1985), LNCS 206, 504–521.

    Google Scholar 

  20. H.J. Prömel and A. Steger, The Steiner Tree Problem. A Tour through Graphs, Algorithms, and Complexity, Vieweg Verlag, Wiesbaden, to appear 1997.

    Google Scholar 

  21. F. Suraweera and P. Bhattacharya, An O(log m) parallel algorithm for the minimum spanning tree problem, Inf. Proc. Lett.45 (1993), 159–163.

    Article  Google Scholar 

  22. H. Takahashi and A. Matsuyama, An approximate solution for the Steiner problem in graphs, Math. Japonica24 (1980), 573–577.

    Google Scholar 

  23. A.Z. Zelikovsky, An 11/6-approximation algorithm for the network Steiner problem, Algorithmica9 (1993), 463–470.

    Article  Google Scholar 

  24. A.Z. Zelikovsky, Better approximation algorithms for the network and Euclidean Steiner tree problems, Technical Report, Kishinev, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt Universität zu Berlin, 10099, Berlin, Germany

    Hans Jürgen Prömel

  2. Institut für Informatik, TU München, 80290, München, Germany

    Angelika Steger

Authors
  1. Hans Jürgen Prömel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angelika Steger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Rüdiger Reischuk Michel Morvan

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Prömel, H.J., Steger, A. (1997). RNC-approximation algorithms for the steiner problem. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023489

Download citation

  • DOI: https://doi.org/10.1007/BFb0023489

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation