Skip to main content
SpringerLink
Log in

Efficient Algorithms for the Minimum Connected Domination on Trapezoid Graphs

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

Included in the following conference series:

  • 430 Accesses

Abstract

Given the trapezoid diagram, the problem of finding the minimum cardinality connected dominating set in trapezoid graphs was solved in O(m+ n) time [7]; the results is recently improved to be O(n) time by Kohler [5]. For the (vertex) weighted case, finding the minimum weighted connected dominating set in trapezoid graphs can be solved in O(m + n log n) time [11]. Here n (m) denotes the number of vertices (edges) of the trapezoid graph.

In this paper, we show a different approach for finding the minimum cardinality connected dominating set in trapezoid graphs using O(n) time. For finding the minimum weighted connected dominating set, we show the problem can be efficiently solved in O(n log log n) time.

The work was partly supported by the National Science Council, Taiwan, R.O.C, grant NSC-88-2213-E-126-005.

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. Andreas Brandstädt, Van Bang Le, and Jeremy P. Spinrad. Graph Classes: A Survey. SIAM monographs on discrete mathematics and applications, Philadelphia, P. A., 1999.

    Google Scholar 

  2. M.-S. Chang. Weighted domination of cocomparability graphs. Discr. Applied Math., 80:135–148, 1997.

    Article  MATH  Google Scholar 

  3. I. Dagan, M.C. Golumbic, and R.Y. Pinter. Trapezoid graphs and their coloring. Discr. Applied Math., 21:35–46, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  4. T.W. Haynes, S.T. Hedetniemi, and P.J. Slater. Fundamentals of Domination in Graphs. Marcel Dekker, Inc., N. Y., 1998.

    MATH  Google Scholar 

  5. E. Kohler. Connected domination and dominating clique in trapezoid graphs. Discr. Applied Math., 99:91–110, 2000.

    Article  MathSciNet  Google Scholar 

  6. D. Kratsch and L. K. Stewart. Domination on cocomparability graphs. SIAM J. Discrete Math., 6(3):400–417, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  7. Y. D. Liang. Steiner set and connected domination in trapezoid graphs. Information Processing Letters, 56(2):101–108, 1995.

    Article  MathSciNet  Google Scholar 

  8. Y. Daniel Liang. Dominations in trapezoid graphs. Information Processing Letters, 52(6):309–315, December 1994.

    Google Scholar 

  9. Yaw-Ling Lin. Fast algorithms for independent domination and efficient domination in trapezoid graphs. In ISAAC’98, LNCS 1533, pages 267–276, Taejon, Korea, December 1998. Springer-Verlag.

    Google Scholar 

  10. T.-H. Ma and J.P. Spinrad. On the 2-chain subgraph cover and related problems. J. Algorithms, 17:251–268, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  11. Anand Srinivasan, M.S. Chang, K. Madhukar, and C. Pandu Rangan. Efficient algorithms for the weighted domination problems on trapezoid graphs. Manuscript, 1996.

    Google Scholar 

  12. P. van Emde Boas. Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters, 6:80–82, 1977.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Providence University, 200 Chung Chi Road, Sa-Lu, Taichung Shang, 433, Taiwan, R.O.C.

    Yaw-Ling Lin

  2. Department of Computer Science and Information Management, Taiwan

    Fang Rong Hsu

  3. Department of Accounting, Taiwan

    Yin-Te Tsai

  4. Department of Computer Science and Information Management, Taiwan

    Yin-Te Tsai

Authors
  1. Yaw-Ling Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fang Rong Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yin-Te Tsai
    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, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lin, YL., Hsu, F.R., Tsai, YT. (2000). Efficient Algorithms for the Minimum Connected Domination on Trapezoid Graphs. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-44968-X_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation