Skip to main content
SpringerLink
Log in

AnFPTAS forWeight-Constrained SteinerTrees in Series-Parallel Graphs

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2108))

Included in the following conference series:

Abstract

In this paper, we study the problem of computing a minimum cost Steiner tree subject to weight constraint in a series-parallel graph where each edge has a nonnegative integer cost and a nonnegative integer weight.We present a fully polynomial time approximation scheme for this NP-complete problem.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. S. Arora, Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems, Journal of the ACM, Vol. 45(1998), pp. 753–782.

    Article  MATH  MathSciNet  Google Scholar 

  2. G.T. Chen and G.L. Xue, K-pair delay constrained minimum cost routing in undirected networks, SODA2001-ACM-SIAM Symposium on Discrete Algorithms, pp. 230–231.

    Google Scholar 

  3. C.J. Colbourn and G. Xue, Grade of service Steiner trees on a series-parallel network, in D.-Z. Du, J.M. Smith, and J.H. Rubinstein (Eds.), Advances in Steiner Trees, Kluwer Academic Publishers, 2000, pp. 163–174.

    Google Scholar 

  4. D.Z. Du and F.K. Hwang, An approach for proving lower bounds: solution of Gilbert-Pollak conjecture on Steiner ratio, IEEE FOCS’90, pp. 76–85.

    Google Scholar 

  5. A.M. Farley, Networks immune to isolated failures, Networks, Vol. 11(1981), pp. 255–268.

    Article  MATH  MathSciNet  Google Scholar 

  6. M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H Freeman and Company, 1979.

    Google Scholar 

  7. R. Hassin, Approximation schemes for the restricted shortest path problem, Mathematics of Operations Research, Vol. 17(1992), pp. 36–42.

    Article  MATH  MathSciNet  Google Scholar 

  8. F.K. Hwang, D.S. Richards and Pawel Winter, The Steiner tree problem, Annals of Discrete Mathematics, Vol. 53, North-Holland, 1992.

    Google Scholar 

  9. O. Ibarra and C. Kim, Fast approximation algorithms for the knapsack and sum of subsets problems, Journal of ACM, Vol. 22, pp. 463–468.

    Google Scholar 

  10. X. Jia and L. Wang, Group multicast routing using multiple minimum Steiner trees, Journal of Computer Communications, pp. 750–758, 1997.

    Google Scholar 

  11. T. Jiang and L. Wang, Computing shortest networks under a fixed topology, in D.-Z. Du, J.M. Smith, and J.H. Rubinstein (Eds.), Advances in Steiner Trees, Kluwer Academic Publishers, 2000, pp. 39–62.

    Google Scholar 

  12. S. Sahni, General techniques for combinatorial approximations, Operations Research, Vol. 35(1977), pp. 70–79.

    MathSciNet  Google Scholar 

  13. J.A. Wald and C.J. Colbourn, Steiner trees, partial 2-trees, and minimum IFI networks, Networks, Vol. 13(1983), pp. 159–167.

    Article  MATH  MathSciNet  Google Scholar 

  14. Zheng Wang and Jon Crowcroft, Quality-of-service routing for supporting multimedia applications, IEEE Journal on Selected Areas in Communications, Vol. 14(1996), pp. 1228–1234.

    Article  Google Scholar 

  15. P. Winter, Generalized Steiner problem in series-parallel networks, J. Algorithms, Vol. 7(1986), pp. 549–566.

    Article  MATH  MathSciNet  Google Scholar 

  16. G.L. Xue, G.H. Lin and D.Z. Du, Grade of service Steiner minimum trees in the Euclidean plane, Algorithmica, accepted for publication.

    Google Scholar 

  17. G.L. Xue and W. Xiao, An FPTAS for minimum cost delay constrained multicast tree under a Steiner topology, with applications, submitted for publication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hongzhou Institute of Electronic Engineering, School of Science and Arts, Hongzhou, China

    Guangting Chen

  2. Department of Computer Science, University of Vermont, Burlington, VT, 05405

    Guoliang Xue

Authors
  1. Guangting Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoliang Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts, One University Avenue, Lowell, MA, 01854, USA

    Jie Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, G., Xue, G. (2001). AnFPTAS forWeight-Constrained SteinerTrees in Series-Parallel Graphs. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_58

Download citation

  • DOI: https://doi.org/10.1007/3-540-44679-6_58

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42494-9

  • Online ISBN: 978-3-540-44679-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation