International Computer Science Symposium in Russia

CSR 2012: Computer Science – Theory and Applications pp 172-183

Broadcast Domination on Block Graphs in Linear Time

  • Pinar Heggernes
  • Sigve H. Sæther
Conference paper

DOI: 10.1007/978-3-642-30642-6_17

Volume 7353 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pinar Heggernes
    • 1
  • Sigve H. Sæther
    • 1
  1. 1.Department of InformaticsUniversity of BergenNorway