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Broadcast Domination on Block Graphs in Linear Time

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

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.

Keywords

  • Short Path
  • Linear Time
  • Interval Graph
  • Domination Number
  • Chordal Graph

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work is supported by the Research Council of Norway.

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© 2012 Springer-Verlag Berlin Heidelberg

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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

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  • 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

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