Skip to main content
SpringerLink
Log in

A Linear-Time Algorithm to Find Independent Spanning Trees in Maximal Planar Graphs

  • Conference paper
  • First Online:
Graph-Theoretic Concepts in Computer Science (WG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1928))

Included in the following conference series:

Abstract

Given a graph G, a designated vertex r and a natural number k, we wish to find k “independent” spanning trees of G rooted at r, that is, k spanning trees such that, for any vertex v, the k paths connecting r and v in the k trees are internally disjoint in G. In this paper we give a linear-time algorithm to find k independent spanning trees in a k-connected maximal planar graph rooted at any designated vertex.

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. F. Bao and Y. Igarashi, Reliable broadcasting in product networks with Byzantine faults, Proc. 26th Annual International Symposium on Fault-Tolelant Computing (FTCS’96) (1996) 262–271.

    Google Scholar 

  2. G. Di Battista, R. Tamassia and L. Vismara, Output-sensitive reporting of disjoint paths, Technical Report CS-96-25, Department of Computer Science, Brown University (1996).

    Google Scholar 

  3. G. Di Battista, R. Tamassia and L. Vismara, Output-sensitive reporting of disjoint paths, Algorithmica, 23(1999) 302–340.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Chrobak and G. Kant, Convex grid drawings of 3-connected planar graphs, Technical Report RUU-CS-93-45, Department of Computer Science, Utrecht University (1993).

    Google Scholar 

  5. M. Chrobak and G. Kant, Convex grid drawings of 3-connected planar graphs, International Journal of Computational Geometry and Applications, 7 (1997) 211–223.

    Article  MathSciNet  Google Scholar 

  6. J. Cheriyan and S. N. Maheshwari, Finding nonseparating induced cycles and independent spanning trees in 3-connected graphs, J. Algorithms, 9 (1988) 507–537.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Dolev, J. Y. Halpern, B. Simons and R. Strong, A new look at fault tolerant network routing, Proc. 16th Annual ACM Symposium on Theory of Computing (1984) 526–535.

    Google Scholar 

  8. S. Even, Graph Algorithms, Computer Science Press, Potomac (1979).

    Google Scholar 

  9. A. Huck, Independent trees in graphs, Graphs and Combinatorics, 10(1994) 29–45.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Huck, Independent trees in planar graphs, Graphs and Combinatorics, 15 (1999) 29–77.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Itai and M. Rodeh, The multi-tree approach to reliability in distributed networks, Information and Computation, 79 (1988) 43–59.

    Article  MATH  MathSciNet  Google Scholar 

  12. C. Kant, Drawing planar graphs using the cononical ordering, Algorithmica, 16 (1996) 4–32.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Kant and X. He, Two algorithms for _nding rectangular duals of planar graphs, Proc. 19th Workshop on Graph-Theoretic Concepts in Computer Science (WG’93), Lect. Notes in Comp. Sci., 790, Springer (1994) 396–410.

    Google Scholar 

  14. S. Khuller and B. Schieber, On independent spanning trees, Information Processing Letters, 42 (1992) 321–323.

    Article  MATH  MathSciNet  Google Scholar 

  15. K. Miura, D. Takahashi, S. Nakano and T. Nishizeki, A Linear-Time Algorithm to Find Four Independent Spanning Trees in Four-Connected Planar Graphs, WG’98, Lect. Notes in Comp. Sci., 1517, Springer (1998) 310–323.

    Google Scholar 

  16. S. Nakano, M. S. Rahman and T. Nishizeki, A linear time algorithm for four-partitioning four-connected planar graphs, Information Processing Letters, 62 (1997) 315–322.

    Article  MathSciNet  Google Scholar 

  17. K. Obokata, Y. Iwasaki, F. Bao and Y. Igarashi, Independent spanning trees of product graphs and their construction, Proc. 22nd Workshop on Graph-Theoretic Concepts in Computer Science (WG’96), Lect. Notes in Comp. Sci., 1197 (1996) 338–351.

    Google Scholar 

  18. W. Schnyder, Embedding planar graphs on the grid, Proc. 1st Annual ACMSIAM Symp. on Discrete Algorithms, San Francisco (1990) 138–148

    Google Scholar 

  19. D. B. West, Introduction to Graph Teory, Prentice Hall (1996)

    Google Scholar 

  20. A. Zehavi and A. Itai, Three tree-paths, J. Graph Theory, 13 (1989) 175–188.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Gunma University, 376-8515, Kiryu, Japan

    Sayaka Nagai & Shin-ichi Nakano

Authors
  1. Sayaka Nagai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shin-ichi Nakano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer and Information Science, University of Konstanz, Box D 188, 78457, Konstanz, Germany

    Ulrik Brandes  & Dorothea Wagner  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nagai, S., Nakano, Si. (2000). A Linear-Time Algorithm to Find Independent Spanning Trees in Maximal Planar Graphs. In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_27

Download citation

  • DOI: https://doi.org/10.1007/3-540-40064-8_27

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41183-3

  • Online ISBN: 978-3-540-40064-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation