Computer Science – Theory and Applications

Volume 7353 of the series Lecture Notes in Computer Science pp 172-183

Broadcast Domination on Block Graphs in Linear Time

  • Pinar HeggernesAffiliated withDepartment of Informatics, University of Bergen
  • , Sigve H. SætherAffiliated withDepartment of Informatics, University of Bergen

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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.