A linear-time algorithm for minimum <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e529" altimg="si17.svg"><mml:mi>k</mml:mi></mml:math>-hop dominating set of a cactus graph

Given a graph G = ( V , E ) and an integer k ? 1 - hop dominating set D of is subset such that, for every vertex v ? there exists node u whose distance from at most . A -hop minimum cardinality called In this paper, we present linear-time algorithm that finds in cactus graphs which improves the O n 3 -time Borradaile Le (2017). To achieve this, show problem unicyclic reduces to piercing circular arcs sorted arcs, best known log algorithm.