Skip to main content
SpringerLink
Log in
Book cover

European Symposium on Algorithms

ESA 1998: Algorithms — ESA’ 98 pp 441–452Cite as

2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1461))

Abstract

We study the problem of finding a spanning tree with maximum number of leaves. We present a simple 2-approximation algorithm for the problem, improving on the approximation ratio of 3 achieved by the best previous algorithms. We also study the variant in which a given set of vertices must be leaves of the spanning tree, and we present a 5/2-approximation algorithm for this version of the problem.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Duckworth W., Dunne P.E., Gibbons A.M., and Zito M.: Leafy spanning trees in hypercubes. Technical Report CTAG-97008 (1997) University of Liverpool.

    Google Scholar 

  2. Feige U.: A threshold of ln n for approximating set-cover. Twenty Eighth ACM Symposium on Theory of Computing (1996) 314–318.

    Google Scholar 

  3. Galbiati G., Maffiol F., and Morzenti A.: A short note on the approximability of the maximum leaves spanning tree problem. Information Processing Letters 52 (1994) 45–49.

    Article  MATH  MathSciNet  Google Scholar 

  4. Griggs J.R., Kleitman D.J., and Shastri A.: Spanning trees with many leaves in cubic graphs. Journal of Graph Theory 13 (1989) 669–695.

    Article  MATH  MathSciNet  Google Scholar 

  5. Guha S. and Khuller S.: Approximation algorithms for connected dominating sets. Proceedings of the Fourth Annual European Symposium on Algorithms (1996) 179–193.

    Google Scholar 

  6. Guha S. and Khuller S.: Improved methods for approximating node weight Steiner trees and connected dominating sets. Technical Report CS-TR-3849 (1997) University of Maryland.

    Google Scholar 

  7. Kleitman D.J. and West D.B.: Spanning trees with many leaves. SIAM Journal on Discrete Mathematics 4 (1991) 99–106.

    Article  MATH  MathSciNet  Google Scholar 

  8. Lu H. and Ravi R.: The power of local optimization: approximation algorithms for maximum-leaf spanning tree. Proceedings of the Thirtieth Annual Allerton Conference on Communication, Control, and Computing (1992) 533–542.

    Google Scholar 

  9. Lu H. and Ravi R.: A near-linear time approximation algorithm for maximum-leaf spanning tree. Technical report CS-96-06 (1996) Brown University.

    Google Scholar 

  10. Payan C., Tchuente M., and Xuong N.H.: Arbres avec un nombre de maximum de sommets pendants. Discrete Mathematics 49 (1984) 267–273.

    Article  MATH  MathSciNet  Google Scholar 

  11. Storer J.A.: Constructing full spanning trees for cubic graphs. Information Processing Letters 13 (1981) 8–11.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max Planck Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Roberto Solis-Oba

Authors
  1. Roberto Solis-Oba
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, I-35131, Padova, Italy

    Gianfranco Bilardi  & Geppino Pucci  & 

  2. Department of Electrical Engineering and Computer Science, The University of Illinois at Chicago, 851 South Morgan Street - 1009 SEO, Chicago, IL, 60607-7053, USA

    Gianfranco Bilardi

  3. Dipartimento di Matematica Applicata e Informatica, Università “Cá Foscari” di Venezia, via Torino 155, I-30173, Venezia Mestre, Italy

    Giuseppe F. Italiano

  4. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, I-35131, Padova, Italy

    Andrea Pietracaprina

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Solis-Oba, R. (1998). 2-Approximation Algorithm for Finding a Spanning Tree with Maximum Number of Leaves. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_37

Download citation

  • DOI: https://doi.org/10.1007/3-540-68530-8_37

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64848-2

  • Online ISBN: 978-3-540-68530-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation