Broadcast Domination on Block Graphs in Linear Time

  • Pinar Heggernes
  • Sigve H. Sæther
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)


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.


Short Path Linear Time Interval Graph Domination Number Chordal Graph 
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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

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