1 research outputs found
A Linear-Time Algorithm for Minimum -Hop Dominating Set of a Cactus Graph
Given a graph and an integer , a -hop dominating set
of is a subset of , such that, for every vertex , there
exists a node whose hop-distance from is at most . A -hop
dominating set of minimum cardinality is called a minimum -hop dominating
set. In this paper, we present linear-time algorithms that find a minimum
-hop dominating set in unicyclic and cactus graphs. To achieve this, we show
that the -dominating set problem on unicycle graph reduces to the piercing
circular arcs problem, and show a linear-time algorithm for piercing sorted
circular arcs, which improves the best known -time algorithm