Broadcast Domination on Block Graphs in Linear Time

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.