A Linear-time Algorithm for Broadcast Domination Problem on Interval Graphs

The broadcast domination problem of a graph G = (V,E) is to find a subset B ⊆ V such that the vertices in V \B can be dominated by some vertex in B. The difference between broadcast domination and classical domination is that each vertex v in B is assigned a power value f(v) where f(v) ≥ 1 and the vertices in distance at most f(v) to v can hear (be dominated by) v. The goal is to find the minimum ∑ v∈B f(v). We improve a previous result on interval graphs from O(n) to linear, where n is the number of vertices in the input graph.