Skip to main content
SpringerLink
Log in

On Minimum Average Stretch Spanning Trees in Polygonal 2-Trees

  • Conference paper
Algorithms and Computation (WALCOM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8344))

Included in the following conference series:

  • 1045 Accesses

Abstract

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n vertices, we present an algorithm to compute a minimum average stretch spanning tree in O(n logn) time. This also finds a minimum fundamental cycle basis in polygonal 2-trees.

Supported by the Indo-Max Planck Centre for Computer Science Programme in the area of Algebraic and Parameterized Complexity for the year 2012 - 2013.

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. Alon, N., Karp, R.M., Peleg, D., West, D.: A graph-theoretic game and its application to the k-server problem. SIAM J. of Comput. 24, 78–100 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science 209(1-2), 1–45 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press (2009)

    Google Scholar 

  4. Deo, N., Prabhu, G., Krishnamoorthy, M.S.: Algorithms for generating fundamental cycles in a graph. ACM Transactions on Math. Software 8, 26–42 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Diestel, R.: Graph Theory, 4th edn. Springer (2010)

    Google Scholar 

  6. Ducharme, M., Labelle, G., Lamathe, C., Leroux, P.: A classification of outerplanar k-gonal 2-trees. In: 19th Intern. Conf. on FPSAC (2007) (appeared as Poster.)

    Google Scholar 

  7. Emek, Y.: k-outerplanar graphs, planar duality, and low stretch spanning trees. Algorithmica 61(1), 141–160 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  8. Emek, Y., Peleg, D.: A tight upper bound on the probabilistic embedding of series-parallel graphs. SIAM J. Discrete Math. 23(4), 1827–1841 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Eppstein, D.: Parallel recognition of series-parallel graphs. Inf. Comput. 98(1), 41–55 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fowler, T., Gessel, I., Labelle, G., Leroux, P.: The specification of 2-trees. Advances in Applied Mathematics 28(2), 145–168 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Galbiati, G., Rizzi, R., Amaldi, E.: On the approximability of the minimum strictly fundamental cycle basis problem. Discrete Appl. Math. 159(4), 187–200 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hubicka, E., Syso, M.: Minimal bases of cycles of a graph. In: Recent Advances in Graph Theory, Second Czech Symposium in Graph Theory, pp. 283–293. Academia, Prague (1975)

    Google Scholar 

  13. Kavitha, T., Liebchen, C., Mehlhorn, K., Michail, D., Rizzi, R., Ueckerdt, T., Zweig, K.A.: Cycle bases in graphs characterization, algorithms, complexity, and applications. Computer Science Review 3(4), 199–243 (2009)

    Article  Google Scholar 

  14. Koh, K.M., Teo, C.P.: Chromaticity of series-parallel graphs. Discrete Mathematics 154(1-3), 289–295 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  15. Labelle, G., Lamathe, C., Leroux, P.: Labelled and unlabelled enumeration of k-gonal 2-trees. J. Comb. Theory, Ser. A 106(2), 193–219 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Liebchen, C., Wünsch, G.: The zoo of tree spanner problems. Discrete Appl. Math. 156, 569–587 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  17. Omoomi, B., Peng, Y.-H.: Chromatic equivalence classes of certain generalized polygon trees, iii. Discrete Mathematics 271(1-3), 223–234 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Peng, Y.-H., Little, C.H.C., Teo, K.L., Wang, H.: Chromatic equivalence classes of certain generalized polygon trees. Discrete Mathematics 172(1-3), 103–114 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ramachandran, V.: Parallel Open Ear Decomposition with Applications to Graph Biconnectivity and Triconnectivity. Morgan Kaufmann (1992)

    Google Scholar 

  20. West, D.B.: Introduction to graph theory, 2nd edn. Prentice-Hall (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Madras, India

    N. S. Narayanaswamy & G. Ramakrishna

Authors
  1. N. S. Narayanaswamy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ramakrishna
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    Sudebkumar Prasant Pal

  2. National Institute of Informatics, 2-1-2 Hitotsubashi, 101-8430, Chiyoda-ku, Tokyo, Japan

    Kunihiko Sadakane

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Narayanaswamy, N.S., Ramakrishna, G. (2014). On Minimum Average Stretch Spanning Trees in Polygonal 2-Trees. In: Pal, S.P., Sadakane, K. (eds) Algorithms and Computation. WALCOM 2014. Lecture Notes in Computer Science, vol 8344. Springer, Cham. https://doi.org/10.1007/978-3-319-04657-0_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-04657-0_29

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04656-3

  • Online ISBN: 978-3-319-04657-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation