Skip to main content
SpringerLink
Log in

Broadcast Domination on Block Graphs in Linear Time

  • Conference paper
Computer Science – Theory and Applications (CSR 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7353))

Included in the following conference series:

Abstract

A broadcast domination on a graph assigns an integer value f(u) ≥ 0 to each vertex u, such that every vertex u with f(u) = 0 is within distance f(v) from a vertex v with f(v) > 0. The Broadcast Domination problem seeks to compute a broadcast domination where the sum of the assigned values is minimized. We show that Broadcast Domination can be solved in linear time on block graphs. For general graphs the best known algorithm runs in time \(\mathcal{O}(n^6)\). For trees and interval graphs, linear-time algorithms are known. As block graphs form a superclass of trees, our result extends the classes of graphs on which this problem is solvable in linear time.

This work is supported by the Research Council of Norway.

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. Bandelt, H.J., Mulder, H.M.: Distance-hereditary graphs. J. Comb. Theor., Ser. B 41, 182–208 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang, R.Y., Peng, S.L.: A linear-time algorithm for broadcast domination problem on interval graphs. In: Proceedings of the 27th Workshop on Combinatorial Mathematics and Computation Theory, pp. 184–188. Providence University, Taichung (2010)

    Google Scholar 

  3. Cockayne, E.J., Herke, S., Mynhardt, C.M.: Broadcasts and domination in trees. Disc. Math. 311, 1235–1246 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dabney, J., Dean, B.C., Hedetniemi, S.T.: A linear-time algorithm for broadcast domination in a tree. Networks 53(2), 160–169 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dunbar, J.E., Erwin, D.J., Haynes, T.W., Hedetniemi, S.M., Hedetniemi, S.T.: Broadcasts in graphs. Disc. Appl. Math. 154(1), 59–75 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Erwin, D.J.: Dominating broadcasts in graphs. Bull. Inst. Comb. Appl. 42, 89–105 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Haynes, T.W., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graphs. Marcel Dekker (1998)

    Google Scholar 

  8. Haynes, T.W., Hedetniemi, S.T., Slater, P.J. (eds.): Domination in Graphs: Advanced Topics. Marcel Dekker (1998)

    Google Scholar 

  9. Hedetniemi, S.T., Laskar, R.C. (eds.): Topics on domination. North Holland (1990)

    Google Scholar 

  10. Heggernes, P., Lokshtanov, D.: Optimal broadcast domination of arbitrary graphs in polynomial time. Disc. Math. 306(24), 3267–3280 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Herke, S., Mynhardt, C.M.: Radial trees. Disc. Math. 309, 5950–5962 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Howorka, E.: On metric properties of certain clique graphs. J. Comb. Theor., Ser. B 27(1), 67–74 (1979)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Norway

    Pinar Heggernes & Sigve H. Sæther

Authors
  1. Pinar Heggernes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sigve H. Sæther
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St.Petersburg, 191023, St. Petersburg, Russia

    Edward A. Hirsch

  2. University of Turku, 20014, Turku, Finland

    Juhani Karhumäki  & Arto Lepistö  & 

  3. Lobachevky State University of Nizhni Novgorod, 603950, Niszhi Novgorod, Russia

    Michail Prilutskii

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Heggernes, P., Sæther, S.H. (2012). Broadcast Domination on Block Graphs in Linear Time. In: Hirsch, E.A., Karhumäki, J., Lepistö, A., Prilutskii, M. (eds) Computer Science – Theory and Applications. CSR 2012. Lecture Notes in Computer Science, vol 7353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30642-6_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30642-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30641-9

  • Online ISBN: 978-3-642-30642-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation